Asymptotically Fully Efficient Fixed-Width Confidence Intervals for a Location Parameter

摘要

Let X1, X2, #x2026; be i.i.d. with distribution functionF(x#x2013; #x3b8;), whereFhas a densityfthat is symmetric about the origin.fis assumed to be unknown. Assume further that the Fisher information is finite. For a given confidence coefficient, a two-stage procedure is proposed that gives an asymptotically consistent fixed-width confidence interval for #x3b8; for which the expected sample size is (asymptotically) as small as possible among all fixed-width confidence intervals based on translation equivariant estimators. The procedure does not depend onFand works under very mild regularity conditions. The results are based on use of Stone's (1975) adaptive maximum likelihood estimators, combined with the use of estimates of the Fisher information (truncated in a certain way) to determine an appropriate sample size.