## Regression Case

Let us generalize some of the estimation methods discussed earlier to the regression situation.

M Estimator. The M estimator is easily generalized to the regression model: It minimizes 2£.i/>[(y, — xJb)/$] with respect to the vector b. Its asymptotic variance-covariance matrix is given by Jo(X, AX)~1X’BX(X’AX)_1, where A and В are diagonal matrices with the tth diagonal elements equal to Ep"[(y, — x’t{f)/s0] and E{p'[(y, — x’tfi)/s0]2}, respectively.

Hill and Holland (1977) did a Monte Carlo study on the regression generalization of Andrews’ M estimator described in (2.3.5). They used s = (2.1) Median (largest T— K+ 1 of|y, — х,’Д|} as the scale factor in the p function,

where 0 is the value of b that minimizes i y, — xt’b|. Actually, their estima

tor, which they ...

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