ADAPTIVE ROBUST ESTIMATION OF LOCATION AND SCALE PARAMETERS OF SYMMETRIC POPULATIONS

A study is made of the following two-step procedure for adaptive robust estimation of the mean (y) and the standard deviation (a) of a symmetric population: (1) Classify the sample as having come from a uniform (U), normal (N), or double exponential (D) population according to one of several criteria based on the sample kurtosis K, Hogg's statistic Q, and the sample likelihoods; (2) Then use the maximum likelihood estimators for the chosen population. The MLE y is unbiased, but the MLE 3 is biased. The debiased MLE a is also considered, as are the estimators Fa and Fa of the canonical scale parameter Fa, where the canonical scale factor F is defined as the multiplier of a such that Fa is the 97.5% point of a population symmetric about zero. Two measures of the performance of the estimators are considered. Results are given of a Monte Carlo study based on N = 5000 random samples of sizes n = 8(4)24 from U, N, D and 14 other symmetric populations. © 1979 by Marcel Dekker, Inc. All rights reserved.