Let (X,Y) be a -valued random vector where the conditional distribution of Y given X=x is a Poisson distribution with mean m(x). We estimate m by a local polynomial kernel estimate defined by maximizing a localized log-likelihood function. We use this estimate of m(x) to estimate the conditional...

Estimation of regression functions from independent and identically distributed data is considered. The L2 error with integration with respect to the design measure is used as an error criterion. Usually in the analysis of the rate of convergence of estimates besides smoothness assumptions on...

Given an independent and identically distributed sample of the distribution of an -valued random vector (X,Y), the problem of estimation of the essential supremum of the corresponding regression function is considered. Estimates are constructed, which converge almost surely to this value...

Let X be an d-valued random variable with unknown density f. Let X1, ..., Xn be i.i.d. random variables drawn from f. The objective is to estimate f(x), where x=(x1, ..., xd). We study the pointwise convergence of two new density estimates, the Hilbert product kernel estimate where...

Let X be an -valued random variable with unknown density f. Let X1,...,Xn be i.i.d. random variables drawn from f. We study the pointwise convergence of a new class of density estimates, of which the most striking member is the Hilbert kernel estimatewhere Vd is the volume of the unit ball in ....

Let (X, Y) be an d--valued regression pair, whereXhas a density andYis bounded. Ifni.i.d. samples are drawn from this distribution, the Nadaraya-Watson kernel regression estimate in dwith Hilbert kernelK(x)=1/||x||dis shown to converge weakly for all such regression pairs. We also show that...

A bound on the expected maximal deviation of averages from their means over a finite space of functions is derived. The usefulness of this new bound is demonstrated by an application in nonparametric regression.

Estimation of univariate regression functions from bounded i.i.d. data is considered. Estimates are defined by minimizing a complexity penalized residual sum of squares over all piecewise polynomials. The integrated squared error of these estimates achieves for piecewise p-smooth regression...

Estimation of multivariate regression functions from i.i.d. data is considered. We construct estimates by empiricalL2-error minimization over data-dependent spaces of polynomial spline functions. For univariate regression function estimation these spaces are spline spaces with data-dependent...