Compromise Maximum Likelihood Estimators for Location

Abstract

Abstract This article describes a new approach for constructing robust location estimators. These estimators are constructed to be nearly optimal in small sample sizes simultaneously for two or more possible underlying shapes of the density of the data. The estimators are weighted averages of the maximum likelihood estimators for the densities considered, where the weights depend on the sample through the likelihood functions. Because of this relationship to the usual MLE's, these estimators are called compromise maximum likelihood estimators (CMLE's). For the CMLE's to exhibit good robustness properties, the densities used to construct the CMLE's should be chosen to, in a sense, “span” a reasonable range of possible underlying distributions of the data encountered in practice. For example, to construct CMLE's with the usual robustness properties, that is, which perform well both for narrow-tailed Gaussian data and for data containing outliers or from wide-tailed distributions, the CMLE's might be constru...