Convergence Rates for the Mean Integrated Squared Errors of Some Nonparametric Density Estimators of Recursive delta-Function Type.

摘要

For estimation of a probability density function f by an empirical function f sub n based on a sample of size n from f, a widely used measure of goodness is the mean integrated squared error. For the well known delta-function type of f sub n, we show that the asymptotic behavior of this measure is essentially unchanged if f sub n is replaced by a recursive version. Also, we characterize this asymptotic behavior under somewhat milder smoothness restrictions on f than previously considered in the literature, at the expense however of adding tail restrictions on f.