Adaptive robust estimation of location and scale parameters of symmetric populations

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Abstract
A study is made of the following two-step procedure for adaptive robust estimation of the mean (μ) and the standard deviation (α) 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 is unbiased, but the MLE is biased. The debiased MLE is also considered, as are the estimators and of the canonical scale parameter Fα, where the canonical scale factor F is defined as the multiplier of a such that Fα 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 U5 N, D and 14 other symmetric populations.

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