MAD-LAD Estimator Notes

MAD-LAD Estimator Notes - MAD/LAD Estimator The minimum...

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MAD/LAD Estimator: The “minimum absolute deviations” or “least absolute deviations” estimator is obtained by solving the following linear programming problem: () 11 1 : sgn LAD LAD LAD ii LAD Min yx yx yx ββ β −= ∑∑ 1 i ; where all variables are written in deviation form (to avoid that pesky intercept term) and sgn( ) refers to the sign function (just take the sign of the terms in parentheses. Thus, if a deviation is (-), then the sgn function returns (-). Plus : an approximate first order condition for this problem illustrates an appealing characteristic. The approximate first order condition is: 1 sgn LAD x Suppose we change one of our y values from a positive number, to an extremely positive number. There is no effect on the estimator as the final term in the first order condition carries only the sign. As long as the sign doesn’t change, there is no effect on the
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