170 The Basics of financial economeTrics
Key Points
■ (^) Robust statistics addresses the problem of obtaining estimates that are
less sensitive to small changes in the basic assumptions of the statistical
models used. It is also useful for separating the contribution of the tails
from the contribution of the body of the data.
■ (^) Identifying robust estimators of regressions is a rather difficult problem.
Different choices of estimators, robust or not, might lead to radically
different estimates of a model’s parameters.
■ (^) The expected values of the regression’s dependent variables are obtained
by multiplying the data and the hat matrix.
■ (^) Leverage points are large values of the hat matrix such that small
changes in the data lead to large changes in expectations.
■ (^) To make a regression robust, the least squares method can be general-
ized by using weighting functions that trim residuals.