The Experts below are selected from a list of 252 Experts worldwide ranked by ideXlab platform
S. Jeyaratnam - One of the best experts on this subject based on the ideXlab platform.
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Robust Confidence interval for the variance
Journal of Statistical Computation and Simulation, 1999Co-Authors: Abdelrahim M. Barham, S. JeyaratnamAbstract:In this paper six Confidence intervals for the variance of a distribution are proposed. Extensive simulation study is performed to evaluate the performance of the intervals. A Confidence interval based on an L-estimate of scale is found to be robust; in otherwords, regardless of the sample size and the distribution considered in the study, its actual probability of coverage is quite close to the specified Confidence Coefficient 1 — α.
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Confidence intervals for the correlation Coefficient
Statistics & Probability Letters, 1992Co-Authors: S. JeyaratnamAbstract:The most popular method of setting Confidence intervals for the correlation Coefficient is based on the normal approximation to the Fisher Z-transformation. In this paper a lesser known and minimally investigated method for the construction of Confidence intervals for the correlation Coefficient is reconsidered. These intervals are established to be conservative and numerically confirmed to be tight in the sense that the actual coverage probability is close to a preset value. For a given sample size and Confidence Coefficient, the interval based on the normal approximation to the Z-transformation either contains the reconsidered interval, or is liberal for at least some values of the population correlation Coefficient.
Hsiuying Wang - One of the best experts on this subject based on the ideXlab platform.
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the monotone boundary property and the full coverage property of Confidence intervals for a binomial proportion
Journal of Statistical Planning and Inference, 2010Co-Authors: Hsiuying WangAbstract:Abstract The methodology for deriving the exact Confidence Coefficient of some Confidence intervals for a binomial proportion is proposed in Wang [2007. Exact Confidence Coefficients of Confidence intervals for a binomial proportion. Statist. Sinica 17, 361–368]. The methodology requires two conditions of Confidence intervals: the monotone boundary property and the full coverage property. In this paper, we show that for some Confidence intervals of a binomial proportion, the two properties hold for any sample size. Based on results presented in this paper, the procedure in Wang [2007. Exact Confidence Coefficients of Confidence intervals for a binomial proportion. Statist. Sinica 17, 361–368] can be directly used to calculate the exact Confidence Coefficients of these Confidence intervals for any fixed sample size.
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Exact average coverage probabilities and Confidence Coefficients of Confidence intervals for discrete distributions
Statistics and Computing, 2009Co-Authors: Hsiuying WangAbstract:For a Confidence interval ( L ( X ), U ( X )) of a parameter θ in one-parameter discrete distributions, the coverage probability is a variable function of θ . The Confidence Coefficient is the infimum of the coverage probabilities, inf _ θ P _ θ ( θ ∈( L ( X ), U ( X ))). Since we do not know which point in the parameter space the infimum coverage probability occurs at, the exact Confidence Coefficients are unknown. Beside Confidence Coefficients, evaluation of a Confidence intervals can be based on the average coverage probability. Usually, the exact average probability is also unknown and it was approximated by taking the mean of the coverage probabilities at some randomly chosen points in the parameter space. In this article, methodologies for computing the exact average coverage probabilities as well as the exact Confidence Coefficients of Confidence intervals for one-parameter discrete distributions are proposed. With these methodologies, both exact values can be derived.
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Exact average coverage probabilities and Confidence Coefficients of Confidence intervals for discrete distributions
Statistics and Computing, 2008Co-Authors: Hsiuying WangAbstract:For a Confidence interval (L(X),U(X)) of a parameter θ in one-parameter discrete distributions, the coverage probability is a variable function of θ. The Confidence Coefficient is the infimum of the coverage probabilities, infθPθ( θe(L(X), U(X))). Since we do not know which point in the parameter space the infimum coverage probability occurs at, the exact Confidence Coefficients are unknown. Beside Confidence Coefficients, evaluation of a Confidence intervals can be based on the average coverage probability. Usually, the exact average probability is also unknown and it was approximated by taking the mean of the coverage probabilities at some randomly chosen points in the parameter space. In this article, methodologies for computing the exact average coverage probabilities as well as the exact Confidence Coefficients of Confidence intervals for one-parameter discrete distributions are proposed. With these methodologies, both exact values can be derived.
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improved Confidence estimators for the multivariate normal Confidence set
2000Co-Authors: Hsiuying WangAbstract:Traditionally, the constant coverage probability estimator, Confidence Coefficient, is used to report the Confidence of a multivariate normal Confidence set. Robinson (1979), Lu and Berger (1989) and Robert and Casella (1994) all showed that there are certain estimators better than the Confidence Coefficient when the number of unknown parameters is greater than 4. In this paper some other better estimators are provided.
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BROWN'S PARADOX IN THE ESTIMATED Confidence APPROACH
The Annals of Statistics, 1999Co-Authors: Hsiuying WangAbstract:A widely held notion of classical conditional theory is that statistical inference in the presence of ancillary statistics should be independent of the distribution of those ancillary statistcs. In this paper, ancillary paradoxes which contradict this notion are presented for two scenarios involving Confidence estimation. These results are related to Brown's ancillary paradox in point estimation. Moreover, the Confidence Coefficient, the usual constant coverage probability estimator, is shown to be inadmissible for Confidence estimation in the multiple regression model with random predictor variables if the dimension of the slope parameters is greater than five. Some estimators better than the Confidence Coefficient are provided in this paper. These new estimators are constructed based on empirical Bayes estimators.
Haroon M. Barakat - One of the best experts on this subject based on the ideXlab platform.
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A Note on the Confidence Region for the Bivariate Co-ordinate-wise Quantiles for Bivariate Data
Kyungpook Mathematical Journal, 2003Co-Authors: Haroon M. Barakat, M. A. El-shandidyAbstract:In this paper we established a family of nonparametric recurrence relations satisfied by the Confidence Coefficient of the Confidence region for the bivariate co-ordinate-wise quantiles for bivariate data.
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On the Confidence region for the bivariate co-ordinate-wise quantiles of the continuous bivariate distribution functions
Statistics & Probability Letters, 2002Co-Authors: Haroon M. BarakatAbstract:In this paper, the distribution-free Confidence region (rectangular) for the vector of the co-ordinate-wise quantiles of a general continuous bivariate distribution function is explicitly derived. This Confidence region, in general, depends on the dependence function. A procedure is suggested which enables one to attach a Confidence Coefficient to the estimate of the Confidence region even if the dependence function is unknown. Moreover, some approximated distribution-free lower bounds, which are independent of the dependence function, of the Confidence Coefficient of this region are derived. Finally, some results of this study are extended to the three-dimensional vector of the co-ordinate-wise quantiles.
Paul Kabaila - One of the best experts on this subject based on the ideXlab platform.
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Confidence Intervals in Regression That Utilize Uncertain Prior Information About a Vector Parameter
Australian & New Zealand Journal of Statistics, 2014Co-Authors: Paul Kabaila, Dilshani TisseraAbstract:Summary Consider a linear regression model with independent normally distributed errors. Suppose that the scalar parameter of interest is a specified linear combination of the components of the regression parameter vector. Also suppose that we have uncertain prior information that a parameter vector, consisting of specified distinct linear combinations of these components, takes a given value. Part of our evaluation of a frequentist Confidence interval for the parameter of interest is the scaled expected length, defined to be the expected length of this Confidence interval divided by the expected length of the standard Confidence interval for this parameter, with the same Confidence Coefficient. We say that a Confidence interval for the parameter of interest utilizes this uncertain prior information if (a) the scaled expected length of this interval is substantially less than one when the prior information is correct, (b) the maximum value of the scaled expected length is not too large and (c) this Confidence interval reverts to the standard Confidence interval, with the same Confidence Coefficient, when the data happen to strongly contradict the prior information. We present a new Confidence interval for a scalar parameter of interest, with specified Confidence Coefficient, that utilizes this uncertain prior information. A factorial experiment with one replicate is used to illustrate the application of this new Confidence interval.
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Simultaneous Confidence Intervals for the Population Cell Means, for Two-by-Two Factorial Data, that Utilize Uncertain Prior Information
Communications in Statistics - Theory and Methods, 2014Co-Authors: Paul Kabaila, Khageswor GiriAbstract:Consider a two-by-two factorial experiment with more than one replicate. Suppose that we have uncertain prior information that the two-factor interaction is zero. We describe new simultaneous frequentist Confidence intervals for the four population cell means, with simultaneous Confidence Coefficient 1 − α, that utilize this prior information in the following sense. These simultaneous Confidence intervals define a cube with expected volume that (a) is relatively small when the two-factor interaction is zero and (b) has maximum value that is not too large. Also, these intervals coincide with the standard simultaneous Confidence intervals obtained by Tukey’s method, with simultaneous Confidence Coefficient 1 − α, when the data strongly contradict the prior information that the two-factor interaction is zero. We illustrate the application of these new simultaneous Confidence intervals to a real data set.
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Simultaneous Confidence intervals for the population cell means, for two-by-two factorial data, that utilize uncertain prior information
arXiv: Methodology, 2008Co-Authors: Paul Kabaila, Khageswor GiriAbstract:Consider a two-by-two factorial experiment with more than 1 replicate. Suppose that we have uncertain prior information that the two-factor interaction is zero. We describe new simultaneous frequentist Confidence intervals for the 4 population cell means, with simultaneous Confidence Coefficient 1-alpha, that utilize this prior information in the following sense. These simultaneous Confidence intervals define a cube with expected volume that (a) is relatively small when the two-factor interaction is zero and (b) has maximum value that is not too large. Also, these intervals coincide with the standard simultaneous Confidence intervals obtained by Tukey's method, with simultaneous Confidence Coefficient 1-alpha, when the data strongly contradict the prior information that the two-factor interaction is zero. We illustrate the application of these new simultaneous Confidence intervals to a real data set.
Khageswor Giri - One of the best experts on this subject based on the ideXlab platform.
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Simultaneous Confidence Intervals for the Population Cell Means, for Two-by-Two Factorial Data, that Utilize Uncertain Prior Information
Communications in Statistics - Theory and Methods, 2014Co-Authors: Paul Kabaila, Khageswor GiriAbstract:Consider a two-by-two factorial experiment with more than one replicate. Suppose that we have uncertain prior information that the two-factor interaction is zero. We describe new simultaneous frequentist Confidence intervals for the four population cell means, with simultaneous Confidence Coefficient 1 − α, that utilize this prior information in the following sense. These simultaneous Confidence intervals define a cube with expected volume that (a) is relatively small when the two-factor interaction is zero and (b) has maximum value that is not too large. Also, these intervals coincide with the standard simultaneous Confidence intervals obtained by Tukey’s method, with simultaneous Confidence Coefficient 1 − α, when the data strongly contradict the prior information that the two-factor interaction is zero. We illustrate the application of these new simultaneous Confidence intervals to a real data set.
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Simultaneous Confidence intervals for the population cell means, for two-by-two factorial data, that utilize uncertain prior information
arXiv: Methodology, 2008Co-Authors: Paul Kabaila, Khageswor GiriAbstract:Consider a two-by-two factorial experiment with more than 1 replicate. Suppose that we have uncertain prior information that the two-factor interaction is zero. We describe new simultaneous frequentist Confidence intervals for the 4 population cell means, with simultaneous Confidence Coefficient 1-alpha, that utilize this prior information in the following sense. These simultaneous Confidence intervals define a cube with expected volume that (a) is relatively small when the two-factor interaction is zero and (b) has maximum value that is not too large. Also, these intervals coincide with the standard simultaneous Confidence intervals obtained by Tukey's method, with simultaneous Confidence Coefficient 1-alpha, when the data strongly contradict the prior information that the two-factor interaction is zero. We illustrate the application of these new simultaneous Confidence intervals to a real data set.