Adaptive choice of mean or median in estimating the center of a symmetric distribution

T L Lai; Herbert Robbins; K F Yu

doi:10.1073/pnas.80.18.5803

. 1983 Sep;80(18):5803–5806. doi: 10.1073/pnas.80.18.5803

Adaptive choice of mean or median in estimating the center of a symmetric distribution

T L Lai ^†, Herbert Robbins ^†, K F Yu ^‡

PMCID: PMC384349 PMID: 16593376

Abstract

An adaptive choice of the sample mean ¯x_n or the sample median m_n is proposed for estimating the center of a symmetric distribution. This choice becomes correct as n → ∞, and in simulation results for finite n it is almost as good as the better of ¯x_n and m_n.

Keywords: sample mean, sample median, adaptive estimation