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Maria Greco - One of the best experts on this subject based on the ideXlab platform.
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matched mismatched and robust Scatter Matrix estimation and hypothesis testing in complex t distributed data
EURASIP Journal on Advances in Signal Processing, 2016Co-Authors: Stefano Fortunati, Fulvio Gini, Maria GrecoAbstract:Scatter Matrix estimation and hypothesis testing are fundamental inference problems in a wide variety of signal processing applications. In this paper, we investigate and compare the matched, mismatched, and robust approaches to solve these problems in the context of the complex elliptically symmetric (CES) distributions. The matched approach is when the estimation and detection algorithms are tailored on the correct data distribution, whereas the mismatched approach refers to the case when the Scatter Matrix estimator and the decision rule are derived under a model assumption that is not correct. The robust approach aims at providing good estimation and detection performance, even if suboptimal, over a large set of possible data models, irrespective of the actual data distribution. Specifically, due to its central importance in both the statistical and engineering applications, we assume for the input data a complex t-distribution. We analyze Scatter Matrix estimators derived under the three different approaches and compare their mean square error (MSE) with the constrained Cramer-Rao bound (CCRB) and the constrained misspecified Cramer-Rao bound (CMCRB). In addition, the detection performance and false alarm rate (FAR) of the various detection algorithms are compared with that of the clairvoyant optimum detector.
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on Scatter Matrix estimation in the presence of unknown extra parameters mismatched scenario
European Signal Processing Conference, 2016Co-Authors: Stefano Fortunati, Fulvio Gini, Maria GrecoAbstract:In this paper, a Constrained Mismatched Maximum Likelihood (CMML) estimator for the joint estimation of the Scatter Matrix and the power of Complex Elliptically Symmetric (CES) distributed vectors is derived under misspecified data models. Specifically, this estimator is obtained by assuming a Normal model while the data are sampled from a complex t-distribution. The convergence point of such CMML estimator is investigated and its Mean Square Error (MSE) compared with the Constrained Misspecified Cramer-Rao Bound (CMCRB).
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the impact of unknown extra parameters on Scatter Matrix estimation and detection performance in complex t distributed data
IEEE Signal Processing Workshop on Statistical Signal Processing, 2016Co-Authors: Stefano Fortunati, Maria Greco, Fulvio GiniAbstract:Scatter Matrix estimation and hypothesis testing in Complex Elliptically Symmetric (CES) distributions often relies on the knowledge of additional parameters characterizing the distribution at hand. In this paper, we investigate the performance of optimal estimation and detection algorithms exploiting low-complexity but suboptimal estimates of the extra parameters under the assumption of t-distributed data. Their performance is also compared with that of robust algorithms, which do not rely on such estimates.
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the misspecified cramer rao bound and its application to Scatter Matrix estimation in complex elliptically symmetric distributions
IEEE Transactions on Signal Processing, 2016Co-Authors: Stefano Fortunati, Fulvio Gini, Maria GrecoAbstract:This paper focuses on the application of recent results on lower bounds under misspecified models to the estimation of the Scatter Matrix of complex elliptically symmetric (CES) distributed random vectors. Buildings upon the original works of Q. H. Vuong [Cramer-Rao Bounds for Misspecified Models, Div. of the Humanities and Social Sci., California Inst. of Technol., Pasadena, CA, USA, Working Paper 652, Oct. 1986] and Richmond–Horowitz [“Parameter Bounds on Estimation Accuracy Under Model Misspecification,” IEEE Trans. Signal Process., vol. 63, no. 9, pp. 2263–2278, May 2015], a lower bound, named misspecified Cramer–Rao bound (MCRB), for the error covariance Matrix of any unbiased (in a proper sense) estimator of a deterministic parameter vector under misspecified models, is introduced. Then, we show how to apply these results to the problem of estimating the Scatter Matrix of CES distributed data under data mismodeling. In particular, the performance of the maximum likelihood (ML) estimator are compared, under mismatched conditions, with the MCRB and with the classical CRB in some relevant study cases.
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maximum likelihood covariance Matrix estimation for complex elliptically symmetric distributions under mismatched conditions
Signal Processing, 2014Co-Authors: Maria Greco, Stefano Fortunati, Fulvio GiniAbstract:This paper deals with the maximum likelihood (ML) estimation of Scatter Matrix of complex elliptically symmetric (CES) distributed data when the hypothesized and the true model belong to the CES family but are different, then under mismatched model condition. Firstly, we derive the Huber limit, or sandwich Matrix expression, for a generic CES model. Then, we compare the performance of mismatched and matched ML estimators to the Huber limit and to the Cramer-Rao lower bound (CRLB) in some relevant study cases.
Fulvio Gini - One of the best experts on this subject based on the ideXlab platform.
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matched mismatched and robust Scatter Matrix estimation and hypothesis testing in complex t distributed data
EURASIP Journal on Advances in Signal Processing, 2016Co-Authors: Stefano Fortunati, Fulvio Gini, Maria GrecoAbstract:Scatter Matrix estimation and hypothesis testing are fundamental inference problems in a wide variety of signal processing applications. In this paper, we investigate and compare the matched, mismatched, and robust approaches to solve these problems in the context of the complex elliptically symmetric (CES) distributions. The matched approach is when the estimation and detection algorithms are tailored on the correct data distribution, whereas the mismatched approach refers to the case when the Scatter Matrix estimator and the decision rule are derived under a model assumption that is not correct. The robust approach aims at providing good estimation and detection performance, even if suboptimal, over a large set of possible data models, irrespective of the actual data distribution. Specifically, due to its central importance in both the statistical and engineering applications, we assume for the input data a complex t-distribution. We analyze Scatter Matrix estimators derived under the three different approaches and compare their mean square error (MSE) with the constrained Cramer-Rao bound (CCRB) and the constrained misspecified Cramer-Rao bound (CMCRB). In addition, the detection performance and false alarm rate (FAR) of the various detection algorithms are compared with that of the clairvoyant optimum detector.
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on Scatter Matrix estimation in the presence of unknown extra parameters mismatched scenario
European Signal Processing Conference, 2016Co-Authors: Stefano Fortunati, Fulvio Gini, Maria GrecoAbstract:In this paper, a Constrained Mismatched Maximum Likelihood (CMML) estimator for the joint estimation of the Scatter Matrix and the power of Complex Elliptically Symmetric (CES) distributed vectors is derived under misspecified data models. Specifically, this estimator is obtained by assuming a Normal model while the data are sampled from a complex t-distribution. The convergence point of such CMML estimator is investigated and its Mean Square Error (MSE) compared with the Constrained Misspecified Cramer-Rao Bound (CMCRB).
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the impact of unknown extra parameters on Scatter Matrix estimation and detection performance in complex t distributed data
IEEE Signal Processing Workshop on Statistical Signal Processing, 2016Co-Authors: Stefano Fortunati, Maria Greco, Fulvio GiniAbstract:Scatter Matrix estimation and hypothesis testing in Complex Elliptically Symmetric (CES) distributions often relies on the knowledge of additional parameters characterizing the distribution at hand. In this paper, we investigate the performance of optimal estimation and detection algorithms exploiting low-complexity but suboptimal estimates of the extra parameters under the assumption of t-distributed data. Their performance is also compared with that of robust algorithms, which do not rely on such estimates.
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the misspecified cramer rao bound and its application to Scatter Matrix estimation in complex elliptically symmetric distributions
IEEE Transactions on Signal Processing, 2016Co-Authors: Stefano Fortunati, Fulvio Gini, Maria GrecoAbstract:This paper focuses on the application of recent results on lower bounds under misspecified models to the estimation of the Scatter Matrix of complex elliptically symmetric (CES) distributed random vectors. Buildings upon the original works of Q. H. Vuong [Cramer-Rao Bounds for Misspecified Models, Div. of the Humanities and Social Sci., California Inst. of Technol., Pasadena, CA, USA, Working Paper 652, Oct. 1986] and Richmond–Horowitz [“Parameter Bounds on Estimation Accuracy Under Model Misspecification,” IEEE Trans. Signal Process., vol. 63, no. 9, pp. 2263–2278, May 2015], a lower bound, named misspecified Cramer–Rao bound (MCRB), for the error covariance Matrix of any unbiased (in a proper sense) estimator of a deterministic parameter vector under misspecified models, is introduced. Then, we show how to apply these results to the problem of estimating the Scatter Matrix of CES distributed data under data mismodeling. In particular, the performance of the maximum likelihood (ML) estimator are compared, under mismatched conditions, with the MCRB and with the classical CRB in some relevant study cases.
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maximum likelihood covariance Matrix estimation for complex elliptically symmetric distributions under mismatched conditions
Signal Processing, 2014Co-Authors: Maria Greco, Stefano Fortunati, Fulvio GiniAbstract:This paper deals with the maximum likelihood (ML) estimation of Scatter Matrix of complex elliptically symmetric (CES) distributed data when the hypothesized and the true model belong to the CES family but are different, then under mismatched model condition. Firstly, we derive the Huber limit, or sandwich Matrix expression, for a generic CES model. Then, we compare the performance of mismatched and matched ML estimators to the Huber limit and to the Cramer-Rao lower bound (CRLB) in some relevant study cases.
Stefano Fortunati - One of the best experts on this subject based on the ideXlab platform.
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matched mismatched and robust Scatter Matrix estimation and hypothesis testing in complex t distributed data
EURASIP Journal on Advances in Signal Processing, 2016Co-Authors: Stefano Fortunati, Fulvio Gini, Maria GrecoAbstract:Scatter Matrix estimation and hypothesis testing are fundamental inference problems in a wide variety of signal processing applications. In this paper, we investigate and compare the matched, mismatched, and robust approaches to solve these problems in the context of the complex elliptically symmetric (CES) distributions. The matched approach is when the estimation and detection algorithms are tailored on the correct data distribution, whereas the mismatched approach refers to the case when the Scatter Matrix estimator and the decision rule are derived under a model assumption that is not correct. The robust approach aims at providing good estimation and detection performance, even if suboptimal, over a large set of possible data models, irrespective of the actual data distribution. Specifically, due to its central importance in both the statistical and engineering applications, we assume for the input data a complex t-distribution. We analyze Scatter Matrix estimators derived under the three different approaches and compare their mean square error (MSE) with the constrained Cramer-Rao bound (CCRB) and the constrained misspecified Cramer-Rao bound (CMCRB). In addition, the detection performance and false alarm rate (FAR) of the various detection algorithms are compared with that of the clairvoyant optimum detector.
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on Scatter Matrix estimation in the presence of unknown extra parameters mismatched scenario
European Signal Processing Conference, 2016Co-Authors: Stefano Fortunati, Fulvio Gini, Maria GrecoAbstract:In this paper, a Constrained Mismatched Maximum Likelihood (CMML) estimator for the joint estimation of the Scatter Matrix and the power of Complex Elliptically Symmetric (CES) distributed vectors is derived under misspecified data models. Specifically, this estimator is obtained by assuming a Normal model while the data are sampled from a complex t-distribution. The convergence point of such CMML estimator is investigated and its Mean Square Error (MSE) compared with the Constrained Misspecified Cramer-Rao Bound (CMCRB).
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the impact of unknown extra parameters on Scatter Matrix estimation and detection performance in complex t distributed data
IEEE Signal Processing Workshop on Statistical Signal Processing, 2016Co-Authors: Stefano Fortunati, Maria Greco, Fulvio GiniAbstract:Scatter Matrix estimation and hypothesis testing in Complex Elliptically Symmetric (CES) distributions often relies on the knowledge of additional parameters characterizing the distribution at hand. In this paper, we investigate the performance of optimal estimation and detection algorithms exploiting low-complexity but suboptimal estimates of the extra parameters under the assumption of t-distributed data. Their performance is also compared with that of robust algorithms, which do not rely on such estimates.
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the misspecified cramer rao bound and its application to Scatter Matrix estimation in complex elliptically symmetric distributions
IEEE Transactions on Signal Processing, 2016Co-Authors: Stefano Fortunati, Fulvio Gini, Maria GrecoAbstract:This paper focuses on the application of recent results on lower bounds under misspecified models to the estimation of the Scatter Matrix of complex elliptically symmetric (CES) distributed random vectors. Buildings upon the original works of Q. H. Vuong [Cramer-Rao Bounds for Misspecified Models, Div. of the Humanities and Social Sci., California Inst. of Technol., Pasadena, CA, USA, Working Paper 652, Oct. 1986] and Richmond–Horowitz [“Parameter Bounds on Estimation Accuracy Under Model Misspecification,” IEEE Trans. Signal Process., vol. 63, no. 9, pp. 2263–2278, May 2015], a lower bound, named misspecified Cramer–Rao bound (MCRB), for the error covariance Matrix of any unbiased (in a proper sense) estimator of a deterministic parameter vector under misspecified models, is introduced. Then, we show how to apply these results to the problem of estimating the Scatter Matrix of CES distributed data under data mismodeling. In particular, the performance of the maximum likelihood (ML) estimator are compared, under mismatched conditions, with the MCRB and with the classical CRB in some relevant study cases.
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maximum likelihood covariance Matrix estimation for complex elliptically symmetric distributions under mismatched conditions
Signal Processing, 2014Co-Authors: Maria Greco, Stefano Fortunati, Fulvio GiniAbstract:This paper deals with the maximum likelihood (ML) estimation of Scatter Matrix of complex elliptically symmetric (CES) distributed data when the hypothesized and the true model belong to the CES family but are different, then under mismatched model condition. Firstly, we derive the Huber limit, or sandwich Matrix expression, for a generic CES model. Then, we compare the performance of mismatched and matched ML estimators to the Huber limit and to the Cramer-Rao lower bound (CRLB) in some relevant study cases.
Gao Shang - One of the best experts on this subject based on the ideXlab platform.
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feature extraction approach based on kernel symmetrical Scatter Matrix space
Computer Engineering, 2011Co-Authors: Lin Qing, Gao ShangAbstract:In order to solve the feature extraction problem of nonlinear small sample sizes present in the traditional Fisher discriminant analysis method,a Matrix transform is proposed on the basis of kernel linear subspace theory,by which a new kernel symmetrical linear subspace of within-class Scatter Matrix is constructed.Two kernel solution spaces derived from the within-class Scatter Matrix and its corresponding symmetrical subspace are respectively utilized to obtain the efficient discriminatory information of the samples.Experimental results conduct on the NUST603 and ORL face databases demonstrate the effectiveness of the proposed method.
Pauliina Ilmonen - One of the best experts on this subject based on the ideXlab platform.
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on asymptotic properties of the Scatter Matrix based estimates for complex valued independent component analysis
Statistics & Probability Letters, 2013Co-Authors: Pauliina IlmonenAbstract:Abstract In this paper, we consider the independent component (IC) model, and the asymptotic properties of the complex valued unmixing Matrix estimates that are based on simultaneous use of two Scatter Matrix functionals.
