Abstract: | This paper presents a method of estimation of an “optimal” smoothing parameter (window width) in kernel estimators for a probability
density. The obtained estimator is calculated directly from observations. By “optimal” smoothing parameters we mean those
parameters which minimize the mean integral square error (MISE) or the integral square error (ISE) of approximation of an
unknown density by the kernel estimator. It is shown that the asymptotic “optimality” properties of the proposed estimator
correspond (with respect to the order) to those of the well-known cross-validation procedure 1, 2].
Translated fromStatisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 67–80, Perm, 1990. |