"Coverage probability and exact inference" by Gaurangadeb Chattopadhyay and Bikas K. Sinha
 

Coverage probability and exact inference

Article Type

Research Article

Publication Title

Journal of Statistical Theory and Practice

Abstract

With reference to “point estimation” of a real-valued parameter Θ involved in the distribution of a real-valued random variable X, we consider a sample size n and an underlying unbiased estimator (Formula presented.) of Θ for every n = k, k + 1, k + 2, . . . ; where k is the minimum sample size needed for existence of unbiased estimator(s) of Θ based on (X1, X2, .... Xk).. We wish to investigate exact small-sample properties of the sequence of estimators considered here. This we study by considering what is termed “coverage probability” (CP) and defined as (Formula presented.). For Θ > 0, we may redefine CP(n,c) as (Formula presented.) since (Formula presented.). When Θ > 0 serves as a scale parameter, bounds to the ratio are more meaningful than bounds to the difference. In either case, it is desired that the sequence CP(n, c) n = k, k + 1, k + 2, ......] behaves like an increasing sequence for every c > 0. We may note in passing that we are asking for a property beyond “consistency” of a sequence of unbiased estimators. As is well known, consistency is a large-sample property. In this article we discuss several interesting features of the behavior of the CP(n,c) in the exact sense.

First Page

93

Last Page

99

DOI

10.1080/15598608.2017.1329674

Publication Date

1-2-2018

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