Triple Sampling Inference Procedures for the Mean of the Normal Distribution When the Population Coefficient of Variation Is Known
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Date
2023-03
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Journal Title
Journal ISSN
Volume Title
Type
Article
Publisher
Multidisciplinary Digital Publishing Institute (MDPI)
Series Info
Symmetry;15, 672
Scientific Journal Rankings
Abstract
This paper discusses the triple sampling inference procedures for the mean of a symmetric
distribution—the normal distribution when the coefficient of variation is known. We use the Searls’
estimator as an initial estimate for the unknown population mean rather than the classical sample
mean. In statistics literature, the normal distribution under investigation underlines almost all the
natural phenomena with applications in many fields. First, we discuss the minimum risk point
estimation problem under a squared error loss function with linear sampling cost. We obtained
all asymptotic results that enhanced finding the second-order asymptotic risk and regret. Second,
we construct a fixed-width confidence interval for the mean that satisfies at least a predetermined
nominal value and find the second-order asymptotic coverage probability. Both estimation problems
are performed under a unified optimal framework. The theoretical results reveal that the performance
of the triple sampling procedure depends on the numerical value of the coefficient of variation—the
smaller the coefficient of variation, the better the performance of the procedure.
Description
Keywords
confidence interval;, minimum risk point estimation;, Searls’ estimator;, triple sampling procedure