Robust Regressive Forecasting under Functional Distortions in a Model

Abstract

Regressive forecasting is investigated under the assumption that the hypothetical parametric model of the regression function admits functional distortions. Explicit expressions of prediction risk (mean-square error) for four main types of distortions, guaranteed risk, and robustness coefficient for the least-squares prediction algorithm are derived. The minimax risk criterion is used to construct a robust prediction algorithm from iteratively computed M-estimates of the parameters of the hypothetical regression function with a special loss function. Results of computer-aided experiments are given.