Nonparametric kernel estimators are widely used in many research areas of statistics. An important nonparametric kernel estimator of a regression function is the Nadaraya-Watson kernel regression estimator which is often obtained by using a fixed bandwidth. However, the adaptive kernel estimators with varying bandwidths are specially used to estimate density of the long-tailed and multi-mod dis...

A large part of the theory of extreme value index estimation is developed for positive extreme value indices. The best-known estimator of a positive extreme value index is probably the Hill estimator. This estimator belongs to the category of moment estimators, but can also be interpreted as a quasimaximum likelihood estimator. It has been generalized to a kernel-type estimator, but this kernel...

We propose a nonparametric discrimination method based on a nonparametric Nadaray-Watson kernel regression type-estimator of the posterior probability that an incoming observed vector is a given class. To overcome the curse of dimensionality of the multivariate kernel density estimate, we introduce a variance stabilizing approach which constructs independent predictor variables. Then, the multi...

length-biased data are widely seen in applications. they are mostly applicable in epidemiological studies or survival analysis in medical researches. here we aim to propose a berry-esseen type bound for the kernel density estimator of this kind of data.the rate of normal convergence in the proposed berry-esseen type theorem is shown to be o(n^(-1/6) ) modulo logarithmic term as n tends to infin...

Di Crescenzo and Longobardi (2002) has been proposed a measure of uncertainty related to past life namely past entropy. The present paper addresses the question of extending this concept to bivariate set-up and study some properties of the proposed measure. It is shown that the proposed measure uniquely determines the distribution function. Characterizations for some bivariate lifetime models a...

Recent advances of kernel methods have yielded a framework for nonparametric statistical inference called RKHS embeddings, in which all probability distributions are represented as elements in a reproducing kernel Hilbert space, namely kernel means. In this paper, we consider the recovery of the information of a distribution from an estimate of the kernel mean, when a Gaussian kernel is used. T...

In robust nonparametric kernel regression context,weprescribemethod to select trimming parameter and bandwidth. Through solving estimating equations, we control outlier effect through combining weighting and trimming. We show asymptotic consistency, establish bias, variance properties and derive asymptotics. © 2016 Elsevier B.V. All rights reserved.

The optimal value of the smoothing parameter of the Kernel estimator can be obtained by the well known Plug-in algorithm. The optimality is realised in the sense of Mean Integrated Square Error (MISE). In this paper, we propose to generalise this algorithm to the case of the difficult problem of the estimation of a distribution which has a bounded support. The proposed algorithm consists in sea...

Abstract We propose a new method to estimate the empirical pricing kernel based on option data. We estimate the pricing kernel nonparametrically by using the ratio of the risk-neutral density estimator and the subjective density estimator. The risk-neutral density is approximated by a weighted kernel density estimator with varying unknown weights for different observations, and the subjective d...