A general Akaike-type criterion for model selection in robust regression. (English) Zbl 0878.62047
Summary: H. Akaike’s procedure [Ann. Inst. Stat. Math. 22, 203-217 (1970; Zbl 0259.62076)] for selecting a model minimises an estimate of the expected squared error in predicting new, independent observations. This selection criterion was designed for models fitted by least squares. A different model-fitting technique, such as least absolute deviation regression, requires an appropriate model selection procedure.
This paper presents a general Akaike-type criterion applicable to a wide variety of loss functions for model fitting. It requires only that the function be convex with a unique minimum, and twice differentiable in expectation. Simulations show that the estimators proposed here well approximate their respective prediction errors.
This paper presents a general Akaike-type criterion applicable to a wide variety of loss functions for model fitting. It requires only that the function be convex with a unique minimum, and twice differentiable in expectation. Simulations show that the estimators proposed here well approximate their respective prediction errors.
MSC:
62J05 | Linear regression; mixed models |
62J99 | Linear inference, regression |
62F10 | Point estimation |
62F35 | Robustness and adaptive procedures (parametric inference) |