Coverage probability and exact inference. (2nd January 2018)

• Record Type: Journal Article
• Authors: Chattopadhyay, Gaurangadeb; Sinha, Bikas K.
• Is Part Of: Journal of statistical theory and practice. Volume 12:Number 1(2018)
• Page Start: 93
• Page End: 99
• Publication Date: 2018-01-02
• Subjects: Point estimation -- unbiasedness -- exact inference -- consistency; 62F10 -- 62F12; 519.505
• DOI: 10.1080/15598608.2017.1329674
• Languages: English
• ISSNs: 1559-8608

Abstract

ABSTRACT: With reference to "point estimation" of a real-valued parameter involved in the distribution of a real-valued random variable X, we consider a sample size n and an underlying unbiased estimator of for every where k is the minimum sample size needed for existence of unbiased estimator(s) of based on . 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 . For, we may redefine as since . When 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 behaves like an increasing sequence for every . 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 in the exact sense.