We study the heteroscedastic partially linear model with an unspecified partial baseline component and a nonparametric variance function. An interesting finding is that the performance of a naive weighted version of the existing estimator could deteriorate when the smooth baseline component is badly estimated. To avoid this, we propose a family of consistent estimators and investigate their asy...

Among different candidate parametric detection functions, it is suggested to use Akaike Information Criterion (AIC) to select the most appropriate one of them to fit line transect data. Four different detection functions are considered in this paper. Two of them are taken to satisfy the shoulder condition assumption and the other two estimators do not satisfy this condition. Once the appropriat...

In this paper uniform consistency of estimators obtained from kernel based local linear estimating equations is obtained. Furthermore it is shown that the rate of convergence is at least n for a suitable choice of bandwidth. These result are used to find asymptotic results for the integral of the estimator. As an application we consider an “inverse probability of missingness reweighted estimati...

A semi-parametric algorithm for identification of Hammerstein systems in the presence of correlated noise is proposed. The procedure is based on the non-parametric kernel regression estimator and the standard least squares. The advantages of the method in comparison with the standard non-parametric approach are discussed. Limit properties of the proposed estimator are studied, and the simulatio...

This paper suggests an estimator of the number of jumps of the jump regression functions. The estimator is based on the diierence between right and left one-sided kernel smoothers. It is proved to be a.s. consistent. Some results about its rate of convergence are also provided.

The consistency of the local kernel density estimator is proved. This nonparametric estimator is distinguished by its use of scaling matrices which are random and which may vary for each sample point. Its applications include adaptive construction of importance sampling functions.

The asymptotically best bandwidth selectors for a kernel density estimator currently require the use of either unappealing higher order kernel pilot estimators or related Fourier transform methods. The point of this paper is to present a methodology which allows the fastest possible rate of convergence with the use of only nonnegative kernel estimators at all stages of the selection process. Th...

In this paper, a kernel estimator of the differential entropy of the mark distribution of a homogeneous Poisson marked point process is proposed. The marks have an absolutely continuous distribution on a compact Riemannian manifold without boundary. L2 and almost surely consistency of this estimator as well as its asymptotic normality are investigated.

The problem of the nonparametric minimax estimation of an innnitely smooth density at a given point, under random censorship, is considered. We establish the exact limiting behavior of the local minimax risk and propose the eecient kernel-type estimator based on the Kaplan-Meier estimator.

Abstract: In this paper we prove large and moderate deviations principles for the recursive kernel estimator of a probability density function and its partial derivatives. Unlike the density estimator, the derivatives estimators exhibit a quadratic behaviour not only for the moderate deviations scale but also for the large deviations one. We provide results both for the pointwise and the unifor...