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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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This note was uploaded on 12/08/2011 for the course ECON 702 taught by Professor Staff during the Spring '08 term at UMass (Amherst).
 Spring '08
 STAFF

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