Improved Asymptotics for Zeros of Kernel Estimates via a Reformulation of the Leadbetter-Cryer Integral

@article{Riedel1997ImprovedAF,
title={Improved Asymptotics for Zeros of Kernel Estimates via a Reformulation of the Leadbetter-Cryer Integral},
author={Kurt S. Riedel},
journal={Statistics \& Probability Letters},
year={1997},
volume={32},
pages={351-356}
}

Given noisy data, function estimation is considered when the unknown function is known a priori to be either convex or concave on each of a small number of regions where the function. When the number… Expand

An asymptotic formula is given for the expected number of modes of a kernel density estimator, and this establishes the rate of convergence of the critically smoothed bandwidth.Expand

Abstract : This report considered the mean number of crossings of an arbitrary curve, in a given time T, by a non-stationary normal process. A formula was obtained for this and sufficient conditions… Expand

A kernel estimate is introduced for obtaining a nonparametric estimate of a regression function, as well as of its derivatives. In many fields of engineering and biomedicine, the estimation of… Expand

Given noisy data, function estimation is considered when the unknown function is known a priori to be either convex or concave on each of a small number of regions where the function. When the number… Expand

In this paper we give asymptotic expansions for the expected number of local extremes and inflection points of kernel density estimates. We argue that these numbers can be used as an indicator for… Expand