Robust Econometrics

x = T(Fn) has the following properties. First, the influence function (1)

Hence, the gross-error sensitivity (2) γ(T, F) = ∞, the local-shift sensitivity
(3) λ(T, F) = 0, and the rejection point (4) ρ(T, F) = ∞. Second, the
maximum-bias (5) is infinite for any ε > 0 since

su_Rp kT {(1 - ε)F + εδx} - T(F)k = su_Rp k - εT(F) + εxk = ∞.

Consequently, the breakdown point (6) of the sample mean x = T(Fn) is
zero, ■(T) = 0.

Thus, none of robustness measures characterizing the change of T under
contamination of data (even infinitesimally small) is finite. This behavior,
typical for LS-based methods, motivated alternative estimators that have the
desirable robust properties. In this section, the M -estimators, S-estimators,
and τ -estimators are discussed as well as some extensions and combination
of these approaches. Even though there is a much wider range of robust esti-
mation principles, we focus on those already studied and adopted in various
areas of econometrics.

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