Uniform Strong Consistency of Rao-Blackwell Distribution Function Estimators

A note on uniform consistency of monotone function estimators

UNIFORM IN BANDWIDTH CONSISTENCY OF KERNEL - TYPE FUNCTION ESTIMATORS By

We introduce a general method to prove uniform in bandwidth consistency of kernel-type function estimators. Examples include the kernel density estimator, the Nadaraya–Watson regression estimator and the conditional empirical process. Our results may be useful to establish uniform consistency of data-driven bandwidth kernel-type function estimators.

Uniform in bandwidth consistency of local polynomial regression function estimators

We generalize a method for proving uniform in bandwidth consistency results for kernel type estimators developed by the two last named authors. Such results are shown to be useful in establishing consistency of local polynomial estimators of the regression function.

Weighted Uniform Consistency of Kernel Density Estimators

Let fn denote a kernel density estimator of a continuous density f in d dimensions, bounded and positive. Let (t) be a positive continuous function such that ‖ f β‖∞ < ∞ for some 0 < β < 1/2. Under natural smoothness conditions, necessary and sufficient conditions for the sequence √ nhn 2| loghn | ‖ (t)(fn(t)−Efn(t))‖∞ to be stochastically bounded and to converge a.s. to a constant are obtained...

1 Rates of Strong Uniform Consistency for Multivariate Kernel Density Estimators

Let fn denote the usual kernel density estimator in several dimensions. It is shown that if {an} is a regular band sequence, K is a bounded square integrable kernel of several variables, satisfying some additional mild conditions ((K1) below), and if the data consist of an i.i.d. sample from a distribution possessing a bounded density f with respect to Lebesgue measure on R, then lim supn→∞ √ n...