Estimation of location parameter within pre-specified error bound with second-order efficient two-stage procedure
DOI:
https://doi.org/10.37920/sasj.2021.55.1.4Keywords:
Asymptotic efficiency, Taylor’s theorem, Two-stage confidence interval procedureAbstract
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.