Admissibility of Confidence Estimators in the Regression Model

In the regression model, we assume that the independent variables are random instead of fixed. Consider the problem of estimating the coverage function of a usual confidence interval for the unknown intercept parameter. In this paper, we consider a case in which the number of unknown parameters is s...

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Bibliographic Details
Published in:Journal of multivariate analysis Vol. 76; no. 2; pp. 267 - 276
Main Author: Wang, Hsiuying
Format: Journal Article
Language:English
Published: San Diego, CA Elsevier Inc 01.02.2001
Elsevier
Series:Journal of Multivariate Analysis
Subjects:
admissibility
ancillary statistic
confidence interval
confidence interval, admissibility, coverage function, the usual coverage probability estimator, ancillary statistic
coverage function
Decision theory
Exact sciences and technology
Mathematics
Nonparametric inference
Parametric inference
Probability and statistics
Sciences and techniques of general use
Statistics
the usual coverage probability estimator
confidence interval, admissibility, coverage function, the usual coverage probability estimator, ancillary statistic
Admissibility
Parameter estimation
Admissible estimator
Statistical theory
Confidence limit
Non parametric estimation
Tolerance limit
Statistical estimation
Statistical decision
Independent variable
Confidence interval
Statistical regression
Regression model
Decision theory
Bayes decision
Random variable
ISSN:0047-259X, 1095-7243
Online Access:Get full text
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Summary:In the regression model, we assume that the independent variables are random instead of fixed. Consider the problem of estimating the coverage function of a usual confidence interval for the unknown intercept parameter. In this paper, we consider a case in which the number of unknown parameters is smaller than 5. We show that the usual constant coverage probability estimator is admissible in the usual sense in this case. Note that this estimator is inadmissible in the usual sense in the other case where the number of unknown parameters is greater than 4.
ISSN:0047-259X
1095-7243
DOI:10.1006/jmva.2000.1912