DATA‐DEPENDENT ESTIMATION OF PREDICTION FUNCTIONS

Abstract

Abstract. The technique of cross‐validation for model selection where the observations have martingale‐like structure is developed. It is argued that cross‐validation works, unaltered, in this more general setting. The specific example of the stationary Markov process is considered in detail. An estimate of the one‐step prediction function of this process is selected from a collection of splines by minimizing the cross‐validatory version of the prediction error. Asymptotic optimality of the estimate is established.