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

Bhargab Chattopadhyay; Swarnali Banerjee

doi:10.37920/sasj.2021.55.1.4

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.