Under appropriate assumptions, expressions describing the asymptotic behavior of the bias and variance of k-nearest neighbor density estimates with weight function w are obtained. The behavior of these estimates is compared with that of kernel estimates. Particular attention is paid to the...

Convolution type kernel estimators such as the Priestley-Chao estimator have been discussed by several authors in the fixed design regression model Yi = g(ti)+ [var epsilon]i, where [var epsilon]i are uncorrelated random errors, ti are fixed design points where measurements are made, and g is...

Given unobservable i.i.d. r.v.'s Mi with c.d.f. F, and observable r.v.'s Yij with E(YijMi) = Mi; we study a nonparametric estimate of F based on the Yij's by conditioning and kernel techniques. This investigation extends previous works of Blischke (1965) and James (1978).

We consider the problem of estimating the shape parameters in the multi- variate Liouville model in the presence of an unknown infinite-dimensional parameter. We propose an ad hoc estimate and show that it is asymptotically efficient.

Almost sure uniform convergence rates for M-smoothers have been obtained by Härdle, Janssen and Serfling (1988) in the case of bounded, continuous and monotone score functions. In this paper, we show that if there is an initial estimator whose error is a.s. uniformly bounded, then the same rate...