Abstract: This paper is concerned with the use of a cross-validation method based on the kernel estimate of the conditional mean for the subset selection of stochastic regressors within the framework of non-linear stochastic regression. Under the assumption that the observations are strictly stationary and absolutely regular, we show that the cross-validatory selection is consistent. Furthermore, two kinds of asymptotic efficiency of the selected model are proved. Both simulated and real data are used as illustrations.
Key words and phrases: Absolutely regular, cross-validation, efficiency, kernel estimation, heteroscedasticity, non-linear stochastic regression, subset selection.