This paper develops a sampling algorithm for bandwidth estimation in a nonparametric regression model with continuous and discrete regressors under an unknown error density. The error density is approximated by the kernel density estimator of the unobserved errors, while the regression function is estimated using the Nadaraya-Watson estimator admitting continuous and discrete regressors. We der...

Abstract: The goal of this paper is to study the bootstrap for the Grenander estimator. The first result is a proof of the inconsistency of the nonparametric bootstrap for the Grenander estimator at a given point. The second result is the development and verification of a bootstrap for the L1 confidence band for the Grenander estimator. As part of this work, kernel estimators are studied as alt...

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.

A data-driven method of choosing the bandwidth, h, of a kernel density estimator is proposed. It is seen that this mean& of selecting h is asymptotically equivalent to taking the h that minimizes a certain weighted version of the mean integrated square error. Thus, for a given kernel function, the bandwidth can be chosen optimally without making precise smoothness assumptions on the underlying ...

Statistical modeling of physical laws connects experiments with mathematical descriptions of natural phenomena. The modeling is based on the probability density of measured variables expressed by experimental data via a kernel estimator. As an objective kernel the scattering function determined by calibration of the instrument is introduced. This function provides for a new definition of experi...

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.

This paper is concerned with the problem of selecting a suitable bandwidth for the presmoothed density estimator from right censored data. An asymptotic expression for the mean integrated squared error (MISE) of this estimator is given, and the smoothing parameters minimizing it are proved to be consistent approximations of the MISE bandwidths. As consequence, a bandwidth selector based on plug...

Research is taking place to find effective algorithms for content-based image representation and description. There is a substantial amount of algorithms available that use visual features (color, shape, texture). Shape feature has attracted much attention from researchers that there are many shape representation and description algorithms in literature. These shape image representation and des...

Various consistency proofs for the kernel density estimator have been developed over the last few decades. Important milestones are the pointwise consistency and almost sure uniform convergence with a fixed bandwidth on the one hand and the rate of convergence with a fixed or even a variable bandwidth on the other hand. While considering global properties of the empirical distribution functions...