Estimation of location parameter within pre-specified error bound with second-order efficient two-stage procedure

Authors

  • Bhargab Chattopadhyay Department of Decision Sciences and Information Systems, Indian Institute of Management Visakhapatnam, Andhra Pradesh, India
  • Swarnali Banerjee Department of Mathematics and Statistics, Loyola University Chicago, Chicago, IL, USA

DOI:

https://doi.org/10.37920/sasj.2021.55.1.4

Keywords:

Asymptotic efficiency, Taylor’s theorem, Two-stage confidence interval procedure

Abstract

This paper develops a general approach for constructing a confidence interval for a parameter of interest with a specified confidence coefficient and a specified width. This is done assuming known a positive lower bound for the unknown nuisance parameter and independence of suitable statistics. Under mild conditions, we develop a modified two-stage procedure which enjoys attractive optimality properties including a second-order efficiency property and asymptotic consistency property. We extend this work for finding a confidence interval for the location parameter of the inverse Gaussian distribution. As an illustration, we developed a modified mean absolute deviation-based procedure in the supplementary section for finding a fixed-width confidence interval for the normal mean.

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Published

2021-03-31

Issue

Section

Research Articles