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Large sample optimality of least squares cross-validation in density estimation. (English) Zbl 0599.62051

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.

MSC:

62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference
62H12 Estimation in multivariate analysis
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