Brown's paradox in the estimated confidence approach

Hsiuying Wang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)610-626
Number of pages17
JournalAnnals of Statistics
Volume27
Issue number2
DOIs
StatePublished - 1 Jan 1999

Keywords

  • Admissibility
  • Ancillary statistic
  • Confidence interval
  • Coverage function
  • The usual constant coverage probability estimator

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