Estimation theory and practice is generally focused on maximum likelihood methodology, which boasts of claims of efficiency and widespread availability in software. Likelihood methods occasionally encounter problems with small sample sizes, or if the data are contaminated with outliers. The first problem can be addressed by regularization methods such as Bayesian estimation; the latter problem can be solved by using robust methodology such as the M-estimator, for example. is a particular example of an M-estimator. This article motivates its special properties and provides detailed examples that take advantage of those properties. Copyright © 2009 John Wiley & Sons, Inc.
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