Large sample optimality of least squares cross-validation in density estimation (Q1080583)

Cross-validatory methods in density estimation have generated considerable interest in recent years. Early methods, however, where shown to produce inconsistent estimators unless the distribution tails are very small. A modification was suggested by Bowman and Rudemo using a least squares cross-validation method. In this paper the author proves that the Bowman-Rudemo method minimizes the integrated square error in an asymptotic sense with tail conditions which are only slightly more severe than the hypothesis of finite variance.