Admissibility of the constant-coverage probability estimator for estimating the coverage function of certain confidence interval

Consider a confidence interval for a randomly chosen linear combination of the elements of the mean vector of a p-dimensional normal distribution. The constant coverage probability is the usual estimator for the coverage function of this interval. Wang (1995) have shown that this estimator is inadmi...

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Published in:Statistics & probability letters Vol. 36; no. 4; pp. 365 - 372
Main Author: Wang, Hsiuying
Format: Journal Article
Language:English
Published: Elsevier B.V 03.01.1998
Elsevier
Series:Statistics & Probability Letters
Subjects:
Admissibility
Confidence interval
Confidence interval Admissibility Coverage function Constant coverage probability estimator
Constant coverage probability estimator
Coverage function
Admissibility
62C15
Coverage function
Constant coverage probability estimator
62C10
Confidence interval
ISSN:0167-7152, 1879-2103
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Abstract Consider a confidence interval for a randomly chosen linear combination of the elements of the mean vector of a p-dimensional normal distribution. The constant coverage probability is the usual estimator for the coverage function of this interval. Wang (1995) have shown that this estimator is inadmissible under the squared error loss, if p ⩾ 5. In this paper, we consider the case where p ⩽ 4 and prove that it is admissible under the same loss.
AbstractList Consider a confidence interval for a randomly chosen linear combination of the elements of the mean vector of a p-dimensional normal distribution. The constant coverage probability is the usual estimator for the coverage function of this interval. Wang (1995) have shown that this estimator is inadmissible under the squared error loss, if p [greater-or-equal, slanted] 5. In this paper, we consider the case where p [less-than-or-equals, slant] 4 and prove that it is admissible under the same loss.
Consider a confidence interval for a randomly chosen linear combination of the elements of the mean vector of a p-dimensional normal distribution. The constant coverage probability is the usual estimator for the coverage function of this interval. Wang (1995) have shown that this estimator is inadmissible under the squared error loss, if p ⩾ 5. In this paper, we consider the case where p ⩽ 4 and prove that it is admissible under the same loss.
Author Wang, Hsiuying
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Issue 4
Keywords Admissibility
62C15
Coverage function
Constant coverage probability estimator
62C10
Confidence interval
Language English
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References Brown (BIB1) 1990; 18
Brown, Hwang (BIB2) 1990
Wang (BIB3) 1995
Wang (10.1016/S0167-7152(97)00083-7_BIB3) 1995
Brown (10.1016/S0167-7152(97)00083-7_BIB2) 1990
Brown (10.1016/S0167-7152(97)00083-7_BIB1) 1990; 18
References_xml – year: 1990
  ident: BIB2
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  publication-title: Proc. 1990 Taipei Symp. in Statistics
– year: 1995
  ident: BIB3
  article-title: Brown's paradox in the estimated confidence approach
  publication-title: Technical Report
– volume: 18
  start-page: 471
  year: 1990
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  ident: BIB1
  article-title: An ancillarity paradox which appears in multiple linear regression (with discussion)
  publication-title: Ann. Statist.
– year: 1995
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  article-title: Brown's paradox in the estimated confidence approach
– volume: 18
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  year: 1990
  ident: 10.1016/S0167-7152(97)00083-7_BIB1
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  doi: 10.1214/aos/1176347602
– year: 1990
  ident: 10.1016/S0167-7152(97)00083-7_BIB2
  article-title: Admissibility of confidence estimators
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Snippet Consider a confidence interval for a randomly chosen linear combination of the elements of the mean vector of a p-dimensional normal distribution. The constant...
Consider a confidence interval for a randomly chosen linear combination of the elements of the mean vector of a p-dimensional normal distribution. The constant...
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StartPage 365
SubjectTerms Admissibility
Confidence interval
Confidence interval Admissibility Coverage function Constant coverage probability estimator
Constant coverage probability estimator
Coverage function
Title Admissibility of the constant-coverage probability estimator for estimating the coverage function of certain confidence interval
URI https://dx.doi.org/10.1016/S0167-7152(97)00083-7
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