A smooth adaptive estimator of the mean of a symmetric or asymmetric distribution

Abstract

We study an adaptive estimate (SA) of the mean of a continuous distribution F based on a quasi-linear combination of order statistics with weights which smoothly adapt to the extremeness of the tail order statistics. SA is based in part on the selector statistic (HG2) of Hogg and Lenth (1984), which has been used widely for estimating the location when F is symmetric. We compare SA to HG2 via Monte Carlo for both symmetric and asymmetric F. We find that SA dominates or ties HG2 for symmetric F with t ₅ or lighter tails, and enjoys robustness to asymmetric F (not possessed by HG2), for which it competes well with the sample mean.

Keywords:

• adaptive inference
• quasi-L-statistics
• mean-squared error efficiency
• bias
• influential observation
• bootstrap