(Least Absolute Deviations) Consider the least absolute deviations (LAD) fitting procedure:

(a) Show that this estimator equals the median in the location model (K = 1, x = 1).

(b) Show that the fitting procedure is equivalent to a linear programming problem, which has the general form min a'x subject to Ax b

(c) Show that the LAD fit has the property

(d) Is the LAD fit a linear one?

(e) Is the LAD fit unique?

(f) Show that the LAD objective function treats an increase in the absolute value of a residual as equivalent to an increase in the absolute value of a smaller residual. Contrast this with the objective function used by OLS.

(g) For what sort of data would you prefer the LAD fit to the OLS fit? *

N BLAD agmine XB B