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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.
Acknowledgment
We are extremely thankful to the referee for taking interest in our study and for offering insightful comments that have helped us revise the article and bring it to a satisfactory level. Much of this version reflects the referee’s extensive and useful suggestions.