We present a robust version of Mallows's C(P) for regression models. I
t is defined by RC(P) = W(P)/sigma2 - (U(P) - V(P)), where W(P) = SIGM
A(i) w(i)2r(i)2 is a weighted residual sum of squares computed from a
robust fit of model P, sigma2 is a robust and consistent estimator of
sigma2 in the full model, and U(P) and V(P) are constants depending on
the weight function and the number of parameters in model P. Good sub
set models are those with RC(P) close to V(P) or smaller than V(P). Wh
en the weights are identically 1, W(P) becomes the residual sum of squ
ares of a least squares fit, and RC(P) reduces to Mallows's C(P). The
robust model selection procedure based on RC(P) allows us to choose th
e models that fit the majority of the data by taking into account the
presence of outliers and possible departures from the normality assump
tion on the error distribution. Together with the classical C(P), the
robust version suggests several models from which we can choose.