An estimator of location for dependent data

Abstract

SUMMARY Asymptotic properties of an estimator of location, J n , which is an asymptotically best linear unbiased estimator for the location parameter of the logistic distribution, are studied for dependent data. It is shown that J n is asymptotically normally distributed for strongly-mixing dependent data. The asymptotic variance of J n is obtained in general and computed for strictly stationary first-order Gaussian autoregressive processes. The performance of J n for dependent data is compared with that of the sample mean and the Hodges-Lehmann estimator, which is also asymptotically best unbiased for the logistic distribution.