The Experts below are selected from a list of 324 Experts worldwide ranked by ideXlab platform
Christian P Robert - One of the best experts on this subject based on the ideXlab platform.
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distance weighted losses for testing and Confidence Set evaluation
Test, 1994Co-Authors: Christian P Robert, George CasellaAbstract:The Neyman-Pearson evaluation of testing procedure is often criticized as yielding a decision that is too crude with respect to the decision space and the loss function. Here, we propose some extensions which take into account the notion of distance from the boundary of the Confidence Set or between the hypotheses. This allows for new evaluation tools, as well as extensions to cases where improper priors could not be used previously. We also reconsider the testing Setup as a whole and incorporate new losses which take into account the model choice aspect of testing.
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improved Confidence statements for the usual multivariate normal Confidence Set
1994Co-Authors: Christian P Robert, George CasellaAbstract:The usual multivariate normal Confidence Set has reported Confidence 1—α, which is equal to its coverage probability. If we take a decision theoretic view, and attempt to estimate the coverage, we find that 1— α is an inadmissible estimator in more than four dimensions. We establish this fact and, moreover, exhibit adaptive Confidence estimators that appear to dominate 1— α. These new Confidence estimators are developed through empirical Bayes arguments and approximations. They allow us to attach Confidence that is uniformly greater than 1— α. We provide necessary conditions, and strong numerical evidence to support our domination claims.
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point estimation and Confidence Set in a parallelism model an empirical bayes approach
Annals of economics and statistics, 1991Co-Authors: Christian P Robert, A Md Ehsanes K SalehAbstract:When several simple regression models are assumed to have similar slopes, empirical Bayes methods can efficiently process tis vague information by estimating the hyperparameters of a conjugate prior. The shrinkage estimators we obtain are shown to be minimax and, furthermore, dominate usual Confidence regions in terms of coverage probability.
George Casella - One of the best experts on this subject based on the ideXlab platform.
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Optimal Confidence Sets, Bioequivalence, and the Limaçon of Pascal
Journal of the American Statistical Association, 1995Co-Authors: Lawrence D. Brown, George Casella, J. T. Gene HwangAbstract:Abstract We begin with a decision-theoretic investigation into Confidence Sets that minimize expected volume at a given parameter value. Such Sets are constructed by inverting a family of uniformly most powerful tests, and hence they also enjoy the optimality property of being uniformly most accurate. In addition, these Sets possess Bayesian optimal volume properties and represent the first case (to our knowledge) of a frequentist 1 – α Confidence Set that possesses a Bayesian optimality property. The hypothesis testing problem that generates these Sets is similar to that encountered in bioequivalence testing. Our Sets are optimal for testing bioequivalence in certain Settings; in the case of the normal distribution, the optimal Set is a curve known as the limacon of Pascal. We illustrate the use of these curves with a biopharmaceutical example.
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distance weighted losses for testing and Confidence Set evaluation
Test, 1994Co-Authors: Christian P Robert, George CasellaAbstract:The Neyman-Pearson evaluation of testing procedure is often criticized as yielding a decision that is too crude with respect to the decision space and the loss function. Here, we propose some extensions which take into account the notion of distance from the boundary of the Confidence Set or between the hypotheses. This allows for new evaluation tools, as well as extensions to cases where improper priors could not be used previously. We also reconsider the testing Setup as a whole and incorporate new losses which take into account the model choice aspect of testing.
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improved Confidence statements for the usual multivariate normal Confidence Set
1994Co-Authors: Christian P Robert, George CasellaAbstract:The usual multivariate normal Confidence Set has reported Confidence 1—α, which is equal to its coverage probability. If we take a decision theoretic view, and attempt to estimate the coverage, we find that 1— α is an inadmissible estimator in more than four dimensions. We establish this fact and, moreover, exhibit adaptive Confidence estimators that appear to dominate 1— α. These new Confidence estimators are developed through empirical Bayes arguments and approximations. They allow us to attach Confidence that is uniformly greater than 1— α. We provide necessary conditions, and strong numerical evidence to support our domination claims.
A Md Ehsanes K Saleh - One of the best experts on this subject based on the ideXlab platform.
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point estimation and Confidence Set in a parallelism model an empirical bayes approach
Annals of economics and statistics, 1991Co-Authors: Christian P Robert, A Md Ehsanes K SalehAbstract:When several simple regression models are assumed to have similar slopes, empirical Bayes methods can efficiently process tis vague information by estimating the hyperparameters of a conjugate prior. The shrinkage estimators we obtain are shown to be minimax and, furthermore, dominate usual Confidence regions in terms of coverage probability.
Frank Bretz - One of the best experts on this subject based on the ideXlab platform.
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computation of an exact Confidence Set for a maximum point of a univariate polynomial function in a given interval
Statistics & Probability Letters, 2017Co-Authors: Sanyu Zhou, Frank BretzAbstract:Construction of a Confidence Set for a maximum point of a function is an important statistical problem. Wan et al. (2015) provided an exact 1−α Confidence Set for a maximum point of a univariate polynomial function in a given interval. In this paper, we give an efficient computational method for computing the Confidence Set of Wan et al. (2015). We demonstrate with two examples that the new method is substantially more efficient than the proposals by Wan et al. (2015). Matlab programs have been written which make the implementation of the new method straightforward.
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Confidence Sets for optimal factor levels of a response surface
Biometrics, 2016Co-Authors: Frank BretzAbstract:Construction of Confidence Sets for the optimal factor levels is an important topic in response surfaces methodology. In Wan et al. (2015), an exact inline image Confidence Set has been provided for a maximum or minimum point (i.e., an optimal factor level) of a univariate polynomial function in a given interval. In this article, the method has been extended to construct an exact inline image Confidence Set for the optimal factor levels of response surfaces. The construction method is readily applied to many parametric and semiparametric regression models involving a quadratic function. A conservative Confidence Set has been provided as an intermediate step in the construction of the exact Confidence Set. Two examples are given to illustrate the application of the Confidence Sets. The comparison between Confidence Sets indicates that our exact Confidence Set is better than the only other Confidence Set available in the statistical literature that guarantees the inline image Confidence level.
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an exact Confidence Set for a maximum point of a univariate polynomial function in a given interval
Technometrics, 2015Co-Authors: Frank BretzAbstract:Construction of a Confidence Set for a maximum point of a function is an important statistical problem which has many applications. In this article, an exact 1 − α Confidence Set is provided for a maximum point of a univariate polynomial function in a given interval. It is shown how the construction method can readily be applied to many parametric and semiparametric regression models involving a univariate polynomial function. Examples are given to illustrate this Confidence Set and to demonstrate that it can be substantially narrower and so better than the only other Confidence Set available in the statistical literature that guarantees 1 − α Confidence level.
Jin Zhang - One of the best experts on this subject based on the ideXlab platform.
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Minimum-volume Confidence Sets for normal linear regression models
Statistics, 2018Co-Authors: Jin ZhangAbstract:ABSTRACTIn this article, we establish the minimum-volume Confidence Sets for normal linear regression models, extending the results in Zhang [Minimum volume Confidence Sets for parameters of normal distributions. Adv Stat Anal. 2017;101:309–320] on building the minimum-volume Confidence Sets for parameters of normal distributions. Compared with classical Confidence Sets, the proposed optimal Confidence Set is proved to have the smallest volume, for whatever Confidence level, sample size and sample data.
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Minimum Volume Confidence Sets for Two-Parameter Exponential Distributions
The American Statistician, 2018Co-Authors: Jin ZhangAbstract:ABSTRACTUnder a reasonable restriction, we create the minimum volume Confidence Set for location and scale parameters of the exponential distribution. Compared to existing methods, none of which has a minimum-area property, the new Confidence Set is significantly the best (most accurate) with smallest volume, for whatever Confidence level, sample size, and sample data.