A general Akaike-type criterion for model selection in robust regression

Akaike's procedure (1970) for selecting a model minimises anestimate of the expected squared error in predicting new, independentobservations. This selection criterion was designed for modelsfitted by least squares. A different model-fitting technique,such as least absolute deviation regression, requires an appropriatemodel selection procedure. This paper presents a general Akaike-typecriterion applicable to a wide variety of loss functions formodel fitting. It requires only that the function be convexwith a unique minimum, and twice differentiable in expectation.Simulations show that the estimators proposed here well approximatetheir respective prediction errors.