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Improved confidence estimators for Fieller's confidence sets
Author(s) -
Tsao C. Andy,
Hwang J. T. Gene
Publication year - 1998
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315512
Subject(s) - frequentist inference , estimator , confidence interval , mathematics , parameter space , statistics , space (punctuation) , confidence distribution , bayesian probability , computer science , bayesian inference , operating system
Fieller's confidence set C F for ratios of location parameters, although of great importance in practice, is often cited as an example to criticize frequentist theory. The reason is that the set can consist of the whole parameter space and yet the confidence is γ = 1 – α in any case. In this paper, we study the problem of constructing data‐dependent estimators better than γ + , A reasonable estimator appears to be γ + , which is one if C F is the whole parameter space and γ otherwise. By using an estimated confidence approach and a squared‐error loss, it is shown that γ + dominates γ. The risk improvement of γ + over γ can be sizable. Also, by numerically comparing γ + with a generalized Bayes estimator γ L , which is shown to be admissible when one or two ratios are concerned, it is shown that γ + is nearly admissible. We also conclude that the common practice of reporting 1 – α only when C F is not the whole parameter space is nearly admissible.