The Experts below are selected from a list of 306 Experts worldwide ranked by ideXlab platform

Sean Meyn - One of the best experts on this subject based on the ideXlab platform.

  • Error exponents for Composite Hypothesis testing with small samples
    2012 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2012
    Co-Authors: Dayu Huang, Sean Meyn
    Abstract:

    We consider the small sample Composite Hypothesis testing problem, where the number of samples n is smaller than the size of the alphabet m. A suitable model for analysis is the high-dimensional model in which both n and m tend to infinity, and n = o(m). We propose a new performance criterion based on large deviation analysis, which generalizes the classical error exponent applicable for large sample problems (in which m = O(n)). The results are: (i) The best achievable probability of error Pe decays as -log(Pe) = (n2/m)(1 + o(1))J for some J >; 0, shown by upper and lower bounds. (ii) A coincidence-based test has non-zero generalized error exponent J, and is optimal in the generalized error exponent of missed detection. (iii) The widely-used Pearson's chi-square test has a zero generalized error exponent. (iv) The contributions (i)-(iii) are established under the assumption that the null Hypothesis is uniform. For the non-uniform case, we propose a new test with nonzero generalized error exponent.

  • Feature selection for Composite Hypothesis testing with small samples: Fundamental limits and algorithms
    2012 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2012
    Co-Authors: Dayu Huang, Sean Meyn
    Abstract:

    This paper considers the problem of feature selection for Composite Hypothesis testing: The goal is to select, from m candidate features, r relevant ones for distinguishing the null Hypothesis from the Composite alternative Hypothesis; the training data are given as L sequences of observations, of which each is an n-sample sequence coming from one distribution in the alternative Hypothesis. What is the fundamental limit for successful feature selection? Are there any algorithms that achieve this limit? We investigate this problem in a small-sample high-dimensional setting, with n = o(m), and obtain a tight pair of achievability and converse results: (i) There exists a function f(L, n, r,m) such that if f(L, n, r,m) ↓ 0, then no asymptotically consistent feature selection algorithm exists; (ii) We propose a feature selection algorithm that is asymptotically consistent whenever f(L, n, r,m) ↑ ∞.

  • ICASSP - Error exponents for Composite Hypothesis testing with small samples
    2012 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2012
    Co-Authors: Dayu Huang, Sean Meyn
    Abstract:

    We consider the small sample Composite Hypothesis testing problem, where the number of samples n is smaller than the size of the alphabet m. A suitable model for analysis is the high-dimensional model in which both n and m tend to infinity, and n = o(m). We propose a new performance criterion based on large deviation analysis, which generalizes the classical error exponent applicable for large sample problems (in which m = O(n)). The results are: (i) The best achievable probability of error Pe decays as −log(P e ) = (n2/m)(1 + o(1))J for some J > 0, shown by upper and lower bounds. (ii) A coincidence-based test has non-zero generalized error exponent J, and is optimal in the generalized error exponent of missed detection. (iii) The widely-used Pearson's chi-square test has a zero generalized error exponent. (iv) The contributions (i)-(iii) are established under the assumption that the null Hypothesis is uniform. For the non-uniform case, we propose a new test with nonzero generalized error exponent.

  • ICASSP - Feature selection for Composite Hypothesis testing with small samples: Fundamental limits and algorithms
    2012 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2012
    Co-Authors: Dayu Huang, Sean Meyn
    Abstract:

    This paper considers the problem of feature selection for Composite Hypothesis testing: The goal is to select, from m candidate features, r relevant ones for distinguishing the null Hypothesis from the Composite alternative Hypothesis; the training data are given as L sequences of observations, of which each is an n-sample sequence coming from one distribution in the alternative Hypothesis. What is the fundamental limit for successful feature selection? Are there any algorithms that achieve this limit? We investigate this problem in a small-sample high-dimensional setting, with n = o(m), and obtain a tight pair of achievability and converse results: (i) There exists a function ƒ(L, n, r,m) such that if ƒ(L, n, r,m) ↓ 0, then no asymptotically consistent feature selection algorithm exists; (ii) We propose a feature selection algorithm that is asymptotically consistent whenever ƒ(L, n, r,m) ↑ ∞.

  • Universal and Composite Hypothesis Testing via Mismatched Divergence
    IEEE Transactions on Information Theory, 2011
    Co-Authors: Jayakrishnan Unnikrishnan, Dayu Huang, Sean Meyn, Amit Surana, Venugopal V. Veeravalli
    Abstract:

    For the universal Hypothesis testing problem, where the goal is to decide between the known null Hypothesis distribution and some other unknown distribution, Hoeffding proposed a universal test in the nineteen sixties. Hoeffding's universal test statistic can be written in terms of Kullback-Leibler (K-L) divergence between the empirical distribution of the observations and the null Hypothesis distribution. In this paper a modification of Hoeffding's test is considered based on a relaxation of the K-L divergence, referred to as the mismatched divergence. The resulting mismatched test is shown to be a generalized likelihood-ratio test (GLRT) for the case where the alternate distribution lies in a parametric family of distributions characterized by a finite-dimensional parameter, i.e., it is a solution to the corresponding Composite Hypothesis testing problem. For certain choices of the alternate distribution, it is shown that both the Hoeffding test and the mismatched test have the same asymptotic performance in terms of error exponents. A consequence of this result is that the GLRT is optimal in differentiating a particular distribution from others in an exponential family. It is also shown that the mismatched test has a significant advantage over the Hoeffding test in terms of finite sample size performance for applications involving large alphabet distributions. This advantage is due to the difference in the asymptotic variances of the two test statistics under the null Hypothesis.

Ali Ghobadzadeh - One of the best experts on this subject based on the ideXlab platform.

  • Generalized Wald Test for Binary Composite Hypothesis Test
    IEEE Signal Processing Letters, 2015
    Co-Authors: Masoud Naderpour, Ali Ghobadzadeh, Ali A. Tadaion, Saeed Gazor
    Abstract:

    This letter provides a generalization of the well-known Wald test. The proposed generalized Wald test (GWT) is a Separating Function Estimation Test (SFET) which is a type of detector recently introduced for a wide class of Composite problems. The test statistics of an SFET is an estimate of a real-valued Separating Function (SF). It is already proved that a Minimum Variance Unbiased Estimator of any SF leads to the optimal Uniformly Most Powerful unbiased detector. In many practical cases, such an optimal detector does not exist; hence, suboptimal ones are used, instead. Selecting an SF with a guaranteed performance is still an open problem which is investigated in this letter. First, we derive a lower bound for the detection probability of the SFET in terms of corresponding SF and the Fisher Information Matrix. Then we optimize the proposed bound with respect to the SF. The solution of the optimization problem leads to a generalization of the Wald test which is asymptotically optimal and reduces to the Wald detector in some special cases. Simulation results show the superiority of the proposed GWT over its counterparts, namely, the Wald test and GLR detector in some examples.

  • Invariance and Optimality of CFAR Detectors in Binary Composite Hypothesis Tests
    IEEE Transactions on Signal Processing, 2014
    Co-Authors: Ali Ghobadzadeh, Ali A. Tadaion, Saeed Gazor, Mohammad Reza Taban, Mohammad S. Moshtaghioun
    Abstract:

    We investigate the relationship between constant false alarm rate (CFAR) and invariant tests. We introduce the minimal invariant group (MIG). We show that for a family of distributions, the unknown parameters are eliminated from the distribution of the maximal invariant statistic under the MIG while the maximum information of the observed signal is preserved. We prove that any invariant test with respect to MIG is CFAR and conversely, for any CFAR test an invariant statistic exists with respect to an MIG under some mild conditions. Moreover for a given CFAR test, we propose a systematic method for deriving an enhanced test, i.e., a function of observations exists such that the likelihood ratio (LR) of the maximal invariant of its MIG gives an enhanced test. Furthermore, we introduce the uniformly most powerful-CFAR (UMP-CFAR) test as the optimal CFAR bound among all CFAR tests. We then prove that the UMP-CFAR test for the minimally invariant Hypothesis testing problem is given by the LR of the maximal invariant under MIG. For some problems, this test (MP-CFAR) depends on the unknown parameters of the alternative Hypothesis, however, provides an upper-performance bound for all suboptimal CFAR tests. We also propose three suboptimal novel CFAR tests among which one is asymptotically optimal.

  • separating function estimation tests a new perspective on binary Composite Hypothesis testing
    IEEE Transactions on Signal Processing, 2012
    Co-Authors: Ali Ghobadzadeh, Ali A. Tadaion, Saeed Gazor, Mohammad Reza Taban, Majid Gazor
    Abstract:

    In this paper, we study some relationships between the detection and estimation theories for a binary Composite Hypothesis test H0 against H1 and a related estimation problem. We start with a one-dimensional (1D) space for the unknown parameter space and one-sided Hypothesis problems and then extend out results into more general cases. For one-sided tests, we show that the uniformly most powerful (UMP) test is achieved by comparing the minimum variance and unbiased estimator (MVUE) of the unknown parameter with a threshold. Thus for the case where the UMP test does not exist, the MVUE of the unknown parameter does not exist either. Therefore for such cases, a good estimator of the unknown parameter is deemed as a good decision statistic for the test. For a more general class of Composite testing with multiple unknown parameters, we prove that the MVUE of a separating function (SF) can serve as the optimal decision statistic for the UMP unbiased test where the SF is continuous, differentiable, positive for all parameters under H1 and is negative for the parameters under H0. We then prove that the UMP unbiased statistic is equal to the MVUE of an SF. In many problems with multiple unknown parameters, the UMP test does not exist. For such cases, we show that if one detector between two detectors has a better receiver operating characteristic (ROC) curve, then using its decision statistic we can estimate the SF more e-accurately, in probability. For example, the SF is the signal-to-noise ratio (SNR) in some problems. These results motivate us to introduce new suboptimal SF-estimator tests (SFETs) which are easy to derive for many problems. Finally, we provide some practical examples to study the relationship between the decision statistic of a test and the estimator of its corresponding SF.

  • Separating Function Estimation Tests: A New Perspective on Binary Composite Hypothesis Testing
    IEEE Transactions on Signal Processing, 2012
    Co-Authors: Ali Ghobadzadeh, Ali A. Tadaion, Saeed Gazor, Mohammad Reza Taban, Majid Gazor
    Abstract:

    In this paper, we study some relationships between the detection and estimation theories for a binary Composite Hypothesis test H0 against H1 and a related estimation problem. We start with a one-dimensional (1D) space for the unknown parameter space and one-sided Hypothesis problems and then extend out results into more general cases. For one-sided tests, we show that the uniformly most powerful (UMP) test is achieved by comparing the minimum variance and unbiased estimator (MVUE) of the unknown parameter with a threshold. Thus for the case where the UMP test does not exist, the MVUE of the unknown parameter does not exist either. Therefore for such cases, a good estimator of the unknown parameter is deemed as a good decision statistic for the test. For a more general class of Composite testing with multiple unknown parameters, we prove that the MVUE of a separating function (SF) can serve as the optimal decision statistic for the UMP unbiased test where the SF is continuous, differentiable, positive for all parameters under H1 and is negative for the parameters under H0. We then prove that the UMP unbiased statistic is equal to the MVUE of an SF. In many problems with multiple unknown parameters, the UMP test does not exist. For such cases, we show that if one detector between two detectors has a better receiver operating characteristic (ROC) curve, then using its decision statistic we can estimate the SF more ε-accurately, in probability. For example, the SF is the signal-to-noise ratio (SNR) in some problems. These results motivate us to introduce new suboptimal SF-estimator tests (SFETs) which are easy to derive for many problems. Finally, we provide some practical examples to study the relationship between the decision statistic of a test and the estimator of its corresponding SF.

  • ISIT - The role of MVU estimator and CRB in binary Composite Hypothesis test
    2009 IEEE International Symposium on Information Theory, 2009
    Co-Authors: Ali Ghobadzadeh, Sayed Jalal Zahabi, Ali A. Tadaion
    Abstract:

    This work presents a new perspective to the relationship between the Composite binary Hypothesis test and the estimation of its unknown parameters, i.e. the Uniformly Most Powerful (UMP) test and the Minimum Variance and Unbiased Estimator(MVUE). We show that for the one-sided binary Composite Hypothesis test, if the UMP test exists, it is nothing but comparing the MVUE for the unknown parameter with a threshold. The paper tries to make a link between the Cramer Rao Bound (CRB) in estimation theory and the UMP performance bound in detection theory. In addition to the intrinsic theoretical interest of such relationship discussed in the paper, it leads us to proposing a novel detection method. For such problems in which the UMP test does not exist, we suggest using a good estimator of the unknown parameter as the decision statistic. The simulation results confirm the idea that the closer we get to the CRB in estimating the unknown parameter, the more we get near to the UMP performance bound in detection.

Majid Gazor - One of the best experts on this subject based on the ideXlab platform.

  • separating function estimation tests a new perspective on binary Composite Hypothesis testing
    IEEE Transactions on Signal Processing, 2012
    Co-Authors: Ali Ghobadzadeh, Ali A. Tadaion, Saeed Gazor, Mohammad Reza Taban, Majid Gazor
    Abstract:

    In this paper, we study some relationships between the detection and estimation theories for a binary Composite Hypothesis test H0 against H1 and a related estimation problem. We start with a one-dimensional (1D) space for the unknown parameter space and one-sided Hypothesis problems and then extend out results into more general cases. For one-sided tests, we show that the uniformly most powerful (UMP) test is achieved by comparing the minimum variance and unbiased estimator (MVUE) of the unknown parameter with a threshold. Thus for the case where the UMP test does not exist, the MVUE of the unknown parameter does not exist either. Therefore for such cases, a good estimator of the unknown parameter is deemed as a good decision statistic for the test. For a more general class of Composite testing with multiple unknown parameters, we prove that the MVUE of a separating function (SF) can serve as the optimal decision statistic for the UMP unbiased test where the SF is continuous, differentiable, positive for all parameters under H1 and is negative for the parameters under H0. We then prove that the UMP unbiased statistic is equal to the MVUE of an SF. In many problems with multiple unknown parameters, the UMP test does not exist. For such cases, we show that if one detector between two detectors has a better receiver operating characteristic (ROC) curve, then using its decision statistic we can estimate the SF more e-accurately, in probability. For example, the SF is the signal-to-noise ratio (SNR) in some problems. These results motivate us to introduce new suboptimal SF-estimator tests (SFETs) which are easy to derive for many problems. Finally, we provide some practical examples to study the relationship between the decision statistic of a test and the estimator of its corresponding SF.

  • Separating Function Estimation Tests: A New Perspective on Binary Composite Hypothesis Testing
    IEEE Transactions on Signal Processing, 2012
    Co-Authors: Ali Ghobadzadeh, Ali A. Tadaion, Saeed Gazor, Mohammad Reza Taban, Majid Gazor
    Abstract:

    In this paper, we study some relationships between the detection and estimation theories for a binary Composite Hypothesis test H0 against H1 and a related estimation problem. We start with a one-dimensional (1D) space for the unknown parameter space and one-sided Hypothesis problems and then extend out results into more general cases. For one-sided tests, we show that the uniformly most powerful (UMP) test is achieved by comparing the minimum variance and unbiased estimator (MVUE) of the unknown parameter with a threshold. Thus for the case where the UMP test does not exist, the MVUE of the unknown parameter does not exist either. Therefore for such cases, a good estimator of the unknown parameter is deemed as a good decision statistic for the test. For a more general class of Composite testing with multiple unknown parameters, we prove that the MVUE of a separating function (SF) can serve as the optimal decision statistic for the UMP unbiased test where the SF is continuous, differentiable, positive for all parameters under H1 and is negative for the parameters under H0. We then prove that the UMP unbiased statistic is equal to the MVUE of an SF. In many problems with multiple unknown parameters, the UMP test does not exist. For such cases, we show that if one detector between two detectors has a better receiver operating characteristic (ROC) curve, then using its decision statistic we can estimate the SF more ε-accurately, in probability. For example, the SF is the signal-to-noise ratio (SNR) in some problems. These results motivate us to introduce new suboptimal SF-estimator tests (SFETs) which are easy to derive for many problems. Finally, we provide some practical examples to study the relationship between the decision statistic of a test and the estimator of its corresponding SF.

Dayu Huang - One of the best experts on this subject based on the ideXlab platform.

  • Error exponents for Composite Hypothesis testing with small samples
    2012 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2012
    Co-Authors: Dayu Huang, Sean Meyn
    Abstract:

    We consider the small sample Composite Hypothesis testing problem, where the number of samples n is smaller than the size of the alphabet m. A suitable model for analysis is the high-dimensional model in which both n and m tend to infinity, and n = o(m). We propose a new performance criterion based on large deviation analysis, which generalizes the classical error exponent applicable for large sample problems (in which m = O(n)). The results are: (i) The best achievable probability of error Pe decays as -log(Pe) = (n2/m)(1 + o(1))J for some J >; 0, shown by upper and lower bounds. (ii) A coincidence-based test has non-zero generalized error exponent J, and is optimal in the generalized error exponent of missed detection. (iii) The widely-used Pearson's chi-square test has a zero generalized error exponent. (iv) The contributions (i)-(iii) are established under the assumption that the null Hypothesis is uniform. For the non-uniform case, we propose a new test with nonzero generalized error exponent.

  • Feature selection for Composite Hypothesis testing with small samples: Fundamental limits and algorithms
    2012 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2012
    Co-Authors: Dayu Huang, Sean Meyn
    Abstract:

    This paper considers the problem of feature selection for Composite Hypothesis testing: The goal is to select, from m candidate features, r relevant ones for distinguishing the null Hypothesis from the Composite alternative Hypothesis; the training data are given as L sequences of observations, of which each is an n-sample sequence coming from one distribution in the alternative Hypothesis. What is the fundamental limit for successful feature selection? Are there any algorithms that achieve this limit? We investigate this problem in a small-sample high-dimensional setting, with n = o(m), and obtain a tight pair of achievability and converse results: (i) There exists a function f(L, n, r,m) such that if f(L, n, r,m) ↓ 0, then no asymptotically consistent feature selection algorithm exists; (ii) We propose a feature selection algorithm that is asymptotically consistent whenever f(L, n, r,m) ↑ ∞.

  • ICASSP - Error exponents for Composite Hypothesis testing with small samples
    2012 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2012
    Co-Authors: Dayu Huang, Sean Meyn
    Abstract:

    We consider the small sample Composite Hypothesis testing problem, where the number of samples n is smaller than the size of the alphabet m. A suitable model for analysis is the high-dimensional model in which both n and m tend to infinity, and n = o(m). We propose a new performance criterion based on large deviation analysis, which generalizes the classical error exponent applicable for large sample problems (in which m = O(n)). The results are: (i) The best achievable probability of error Pe decays as −log(P e ) = (n2/m)(1 + o(1))J for some J > 0, shown by upper and lower bounds. (ii) A coincidence-based test has non-zero generalized error exponent J, and is optimal in the generalized error exponent of missed detection. (iii) The widely-used Pearson's chi-square test has a zero generalized error exponent. (iv) The contributions (i)-(iii) are established under the assumption that the null Hypothesis is uniform. For the non-uniform case, we propose a new test with nonzero generalized error exponent.

  • ICASSP - Feature selection for Composite Hypothesis testing with small samples: Fundamental limits and algorithms
    2012 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2012
    Co-Authors: Dayu Huang, Sean Meyn
    Abstract:

    This paper considers the problem of feature selection for Composite Hypothesis testing: The goal is to select, from m candidate features, r relevant ones for distinguishing the null Hypothesis from the Composite alternative Hypothesis; the training data are given as L sequences of observations, of which each is an n-sample sequence coming from one distribution in the alternative Hypothesis. What is the fundamental limit for successful feature selection? Are there any algorithms that achieve this limit? We investigate this problem in a small-sample high-dimensional setting, with n = o(m), and obtain a tight pair of achievability and converse results: (i) There exists a function ƒ(L, n, r,m) such that if ƒ(L, n, r,m) ↓ 0, then no asymptotically consistent feature selection algorithm exists; (ii) We propose a feature selection algorithm that is asymptotically consistent whenever ƒ(L, n, r,m) ↑ ∞.

  • Universal and Composite Hypothesis Testing via Mismatched Divergence
    IEEE Transactions on Information Theory, 2011
    Co-Authors: Jayakrishnan Unnikrishnan, Dayu Huang, Sean Meyn, Amit Surana, Venugopal V. Veeravalli
    Abstract:

    For the universal Hypothesis testing problem, where the goal is to decide between the known null Hypothesis distribution and some other unknown distribution, Hoeffding proposed a universal test in the nineteen sixties. Hoeffding's universal test statistic can be written in terms of Kullback-Leibler (K-L) divergence between the empirical distribution of the observations and the null Hypothesis distribution. In this paper a modification of Hoeffding's test is considered based on a relaxation of the K-L divergence, referred to as the mismatched divergence. The resulting mismatched test is shown to be a generalized likelihood-ratio test (GLRT) for the case where the alternate distribution lies in a parametric family of distributions characterized by a finite-dimensional parameter, i.e., it is a solution to the corresponding Composite Hypothesis testing problem. For certain choices of the alternate distribution, it is shown that both the Hoeffding test and the mismatched test have the same asymptotic performance in terms of error exponents. A consequence of this result is that the GLRT is optimal in differentiating a particular distribution from others in an exponential family. It is also shown that the mismatched test has a significant advantage over the Hoeffding test in terms of finite sample size performance for applications involving large alphabet distributions. This advantage is due to the difference in the asymptotic variances of the two test statistics under the null Hypothesis.

Ali A. Tadaion - One of the best experts on this subject based on the ideXlab platform.

  • Generalized Wald Test for Binary Composite Hypothesis Test
    IEEE Signal Processing Letters, 2015
    Co-Authors: Masoud Naderpour, Ali Ghobadzadeh, Ali A. Tadaion, Saeed Gazor
    Abstract:

    This letter provides a generalization of the well-known Wald test. The proposed generalized Wald test (GWT) is a Separating Function Estimation Test (SFET) which is a type of detector recently introduced for a wide class of Composite problems. The test statistics of an SFET is an estimate of a real-valued Separating Function (SF). It is already proved that a Minimum Variance Unbiased Estimator of any SF leads to the optimal Uniformly Most Powerful unbiased detector. In many practical cases, such an optimal detector does not exist; hence, suboptimal ones are used, instead. Selecting an SF with a guaranteed performance is still an open problem which is investigated in this letter. First, we derive a lower bound for the detection probability of the SFET in terms of corresponding SF and the Fisher Information Matrix. Then we optimize the proposed bound with respect to the SF. The solution of the optimization problem leads to a generalization of the Wald test which is asymptotically optimal and reduces to the Wald detector in some special cases. Simulation results show the superiority of the proposed GWT over its counterparts, namely, the Wald test and GLR detector in some examples.

  • Invariance and Optimality of CFAR Detectors in Binary Composite Hypothesis Tests
    IEEE Transactions on Signal Processing, 2014
    Co-Authors: Ali Ghobadzadeh, Ali A. Tadaion, Saeed Gazor, Mohammad Reza Taban, Mohammad S. Moshtaghioun
    Abstract:

    We investigate the relationship between constant false alarm rate (CFAR) and invariant tests. We introduce the minimal invariant group (MIG). We show that for a family of distributions, the unknown parameters are eliminated from the distribution of the maximal invariant statistic under the MIG while the maximum information of the observed signal is preserved. We prove that any invariant test with respect to MIG is CFAR and conversely, for any CFAR test an invariant statistic exists with respect to an MIG under some mild conditions. Moreover for a given CFAR test, we propose a systematic method for deriving an enhanced test, i.e., a function of observations exists such that the likelihood ratio (LR) of the maximal invariant of its MIG gives an enhanced test. Furthermore, we introduce the uniformly most powerful-CFAR (UMP-CFAR) test as the optimal CFAR bound among all CFAR tests. We then prove that the UMP-CFAR test for the minimally invariant Hypothesis testing problem is given by the LR of the maximal invariant under MIG. For some problems, this test (MP-CFAR) depends on the unknown parameters of the alternative Hypothesis, however, provides an upper-performance bound for all suboptimal CFAR tests. We also propose three suboptimal novel CFAR tests among which one is asymptotically optimal.

  • separating function estimation tests a new perspective on binary Composite Hypothesis testing
    IEEE Transactions on Signal Processing, 2012
    Co-Authors: Ali Ghobadzadeh, Ali A. Tadaion, Saeed Gazor, Mohammad Reza Taban, Majid Gazor
    Abstract:

    In this paper, we study some relationships between the detection and estimation theories for a binary Composite Hypothesis test H0 against H1 and a related estimation problem. We start with a one-dimensional (1D) space for the unknown parameter space and one-sided Hypothesis problems and then extend out results into more general cases. For one-sided tests, we show that the uniformly most powerful (UMP) test is achieved by comparing the minimum variance and unbiased estimator (MVUE) of the unknown parameter with a threshold. Thus for the case where the UMP test does not exist, the MVUE of the unknown parameter does not exist either. Therefore for such cases, a good estimator of the unknown parameter is deemed as a good decision statistic for the test. For a more general class of Composite testing with multiple unknown parameters, we prove that the MVUE of a separating function (SF) can serve as the optimal decision statistic for the UMP unbiased test where the SF is continuous, differentiable, positive for all parameters under H1 and is negative for the parameters under H0. We then prove that the UMP unbiased statistic is equal to the MVUE of an SF. In many problems with multiple unknown parameters, the UMP test does not exist. For such cases, we show that if one detector between two detectors has a better receiver operating characteristic (ROC) curve, then using its decision statistic we can estimate the SF more e-accurately, in probability. For example, the SF is the signal-to-noise ratio (SNR) in some problems. These results motivate us to introduce new suboptimal SF-estimator tests (SFETs) which are easy to derive for many problems. Finally, we provide some practical examples to study the relationship between the decision statistic of a test and the estimator of its corresponding SF.

  • Separating Function Estimation Tests: A New Perspective on Binary Composite Hypothesis Testing
    IEEE Transactions on Signal Processing, 2012
    Co-Authors: Ali Ghobadzadeh, Ali A. Tadaion, Saeed Gazor, Mohammad Reza Taban, Majid Gazor
    Abstract:

    In this paper, we study some relationships between the detection and estimation theories for a binary Composite Hypothesis test H0 against H1 and a related estimation problem. We start with a one-dimensional (1D) space for the unknown parameter space and one-sided Hypothesis problems and then extend out results into more general cases. For one-sided tests, we show that the uniformly most powerful (UMP) test is achieved by comparing the minimum variance and unbiased estimator (MVUE) of the unknown parameter with a threshold. Thus for the case where the UMP test does not exist, the MVUE of the unknown parameter does not exist either. Therefore for such cases, a good estimator of the unknown parameter is deemed as a good decision statistic for the test. For a more general class of Composite testing with multiple unknown parameters, we prove that the MVUE of a separating function (SF) can serve as the optimal decision statistic for the UMP unbiased test where the SF is continuous, differentiable, positive for all parameters under H1 and is negative for the parameters under H0. We then prove that the UMP unbiased statistic is equal to the MVUE of an SF. In many problems with multiple unknown parameters, the UMP test does not exist. For such cases, we show that if one detector between two detectors has a better receiver operating characteristic (ROC) curve, then using its decision statistic we can estimate the SF more ε-accurately, in probability. For example, the SF is the signal-to-noise ratio (SNR) in some problems. These results motivate us to introduce new suboptimal SF-estimator tests (SFETs) which are easy to derive for many problems. Finally, we provide some practical examples to study the relationship between the decision statistic of a test and the estimator of its corresponding SF.

  • ISIT - The role of MVU estimator and CRB in binary Composite Hypothesis test
    2009 IEEE International Symposium on Information Theory, 2009
    Co-Authors: Ali Ghobadzadeh, Sayed Jalal Zahabi, Ali A. Tadaion
    Abstract:

    This work presents a new perspective to the relationship between the Composite binary Hypothesis test and the estimation of its unknown parameters, i.e. the Uniformly Most Powerful (UMP) test and the Minimum Variance and Unbiased Estimator(MVUE). We show that for the one-sided binary Composite Hypothesis test, if the UMP test exists, it is nothing but comparing the MVUE for the unknown parameter with a threshold. The paper tries to make a link between the Cramer Rao Bound (CRB) in estimation theory and the UMP performance bound in detection theory. In addition to the intrinsic theoretical interest of such relationship discussed in the paper, it leads us to proposing a novel detection method. For such problems in which the UMP test does not exist, we suggest using a good estimator of the unknown parameter as the decision statistic. The simulation results confirm the idea that the closer we get to the CRB in estimating the unknown parameter, the more we get near to the UMP performance bound in detection.