Let <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$\mathcal{M }_{\underline{i}}$$</EquationSource> </InlineEquation> be an exponential family of densities on <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$[0,1]$$</EquationSource> </InlineEquation> pertaining to a vector of orthonormal functions <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$$b_{\underline{i}}=(b_{i_1}(x),\ldots ,b_{i_p}(x))^\mathbf{T}$$</EquationSource> </InlineEquation> and consider a problem of estimating a density <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$$f$$</EquationSource> </InlineEquation> belonging to such family for...</equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation>

In this paper a class of estimators of a screening threshold in a nonparametric positive dependence model is introduced and the strong consistency of its members is investigated.

We treat the problem of a data-dependent bandwidth choice for kernel estimation of a density. The difference between the kernel estimate using MSE-optimal bandwidth h0 and its counterpart incorporating natural adaptive estimate is shown to be of order OP(n). This extends Krieger and Pickands...

We consider a strictly stationary long-range-dependent process (Zi)i=1[infinity] with standard exponential marginals and its subordinated process (G(Zi))i=1[infinity] for some real function G. We prove that, analogously to the case of Gaussian subordination, the asymptotic behaviour of...

Hall and Hart (1990) proved that the mean integrated squared error (MISE) of a marginal kernel density estimator from an infinite moving average process X1, X2, ... may be decomposed into the sum of MISE of the same kernel estimator for a random sample of the same size and a term proportional to...

We consider nonparametric prediction problem for both short- and long-range-dependent linear processes. Asymptotic properties of local linear estimates are obtained and, for long-range-dependent processes, an interesting dichotomous phenomenon is described: the limiting distribution depends on...

Asymptotic confidence bands for a density function in case of censored data based on nearest neighbor estimators are constructed. The approach is based on the invariance principle for the kernel estimator with deterministic bandwidths proved by Burke and Horváth.

The method of choosing a smoothing parameter for a grade density kernel estimate g is proposed. It consists in estimating the minimizer of the asymptotic MISE for two main terms in the expansion of g. The behaviour of the estimates incorporating proposed bandwidths is investigated in the variety...

We consider a problem of estimating a conditional variance function of an autoregressive process. A finite collection of parametric models for conditional density is studied when both regression and variance are modelled by parametric functions. The proposed estimators are defined as the maximum...