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### -estimates for Regression

In 1988, Yohai and Zamar introduced the class of -estimates. Assume the linear model (8) and consider two functions . For each define the estimate of the scale of the residuals by

where is the M-scale of the residuals calculated using the function . The -estimates for regression are then defined as

In particular, is an efficient and robust estimate of . As before, under certain regularity conditions (which include symmetry of the distribution of the residuals) we get strong consistency of these estimates and asymptotic normality.

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2000-05-29