Parametric Empirical Bayes Confidence Intervals Based on James-Stein Estimator

He, Kun

doi:10.1524/strm.1992.10.12.121

Cited by 11 publications

(24 citation statements)

References 4 publications

(6 reference statements)

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“…In some cases, it is possible to derive CIs without taking a detour via projections of the confidence region: For the empirical Bayes region of 3.3.5, He showed how to construct corresponding simultaneous CIs for the p parameters directly. This method has recently attracted some attention in the context of selected parameters() and was extended to the unknown variance case…”

Section: Methodsmentioning

confidence: 99%

Simultaneous confidence regions for multivariate bioequivalence

Pallmann

Jaki

2017

Statistics in Medicine

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Demonstrating bioequivalence of several pharmacokinetic (PK) parameters, such as AUC and C , that are calculated from the same biological sample measurements is in fact a multivariate problem, even though this is neglected by most practitioners and regulatory bodies, who typically settle for separate univariate analyses. We believe, however, that a truly multivariate evaluation of all PK measures simultaneously is clearly more adequate. In this paper, we review methods to construct joint confidence regions around multivariate normal means and investigate their usefulness in simultaneous bioequivalence problems via simulation. Some of them work well for idealised scenarios but break down when faced with real-data challenges such as unknown variance and correlation among the PK parameters. We study the shapes of the confidence regions resulting from different methods, discuss how marginal simultaneous confidence intervals for the individual PK measures can be derived, and illustrate the application to data from a trial on ticlopidine hydrochloride. An R package is available.

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Section: Methodsmentioning

confidence: 99%

Simultaneous confidence regions for multivariate bioequivalence

Pallmann

Jaki

2017

Statistics in Medicine

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“…Hence, one needs to replaceτ 2 by max(τ 2 , τ 2 0 ), where τ 2 0 is a positive number. He (1992), Qiu and Hwang (2007), and Hwang, Qiu, and Zhao (2009) all employed some kind of truncation. In particular, the last two articles propose a systematic way to derive the truncation point τ 2 0 .…”

Section: Dealing With the Unknown σ 2 Imentioning

confidence: 99%

Empirical Bayes Confidence Intervals for Selected Parameters in High-Dimensional Data

Hwang

Zhao

2013

Journal of the American Statistical Association

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Modern statistical problems often involve a large number of populations and hence a large number of parameters that characterize these populations. It is common for scientists to use data to select the most significant populations, such as those with the largest t statistics. The scientific interest often lies in studying and making inferences regarding these parameters, called the selected parameters, corresponding to the selected populations. The current statistical practices either apply a traditional procedure assuming there were no selection-a practice that is not valid-or they use the Bonferroni-type procedure that is valid but very conservative and often noninformative. In this article, we propose valid and sharp confidence intervals that allow scientists to select parameters and to make inferences for the selected parameters based on the same data. This type of confidence interval allows the users to zero in on the most interesting selected parameters without collecting more data. The validity of confidence intervals is defined as the controlling of Bayes coverage probability so that it is no less than a nominal level uniformly over a class of prior distributions for the parameter. When a mixed model is assumed and the random effects are the key parameters, this validity criterion is exactly the frequentist criterion, since the Bayes coverage probability is identical to the frequentist coverage probability. Assuming that the observations are normally distributed with unequal and unknown variances, we select parameters with the largest t statistics. We then construct sharp empirical Bayes confidence intervals for these selected parameters, which have either a large Bayes coverage probability or a small Bayes false coverage rate uniformly for a class of priors. Our intervals, applicable to any high-dimensional data, are applied to microarray data and are shown to be better than all the alternatives. It is also anticipated that the same intervals would be valid for any selection rule. Supplementary materials for this article are available online.

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“…In the canonical model He (1992) proved that there exists an interval that dominates I 0 X . Precisely, for δ + (X) of (6), it was shown that there exists a > 0 such that the interval δ + i (X) ± c has higher Bayes coverage probability for any τ 2 > 0.…”

Section: Empirical Bayes Intervalsmentioning

confidence: 99%

“…For the construction of confidence intervals, Qiu and Hwang (2007) adapted the approach of Casella and Hwang (1983) and He (1992) to this problem. For any selection, they constructed 1 − α empirical Bayes confidence intervals for θ (i) which are shown numerically to have confidence coefficient 1−α when σ i = σ is either known or estimable.…”

Section: Intervals For the Selected Meanmentioning

confidence: 99%

Shrinkage Confidence Procedures

Casella¹,

Hwang²

2012

Statist. Sci.

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The possibility of improving on the usual multivariate normal confidence was first discussed in Stein (1962). Using the ideas of shrinkage, through Bayesian and empirical Bayesian arguments, domination results, both analytic and numerical, have been obtained. Here we trace some of the developments in confidence set estimation.Comment: Published in at http://dx.doi.org/10.1214/10-STS319 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

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Parametric Empirical Bayes Confidence Intervals Based on James-Stein Estimator

Cited by 11 publications

References 4 publications

Simultaneous confidence regions for multivariate bioequivalence

Simultaneous confidence regions for multivariate bioequivalence

Empirical Bayes Confidence Intervals for Selected Parameters in High-Dimensional Data

Shrinkage Confidence Procedures

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