Asymptotic normality for density kernel estimators in discrete and continuous time
type: Item
instance of: scholarly article
title: Asymptotic normality for density kernel estimators in discrete and continuous time
zbMATH Open document ID: 0926.60024
author: Florence Merlevède
author: Magda Peligrad
author: Denis Bosq
published in: Journal of Multivariate Analysis
publication date: 1999-11-29T00:00:00Z
review text: A central limit theorem for double arrays of \(\alpha\)-mixing sequences is established and applied to kernel density estimators for both discrete and continuous time stochastic processes. There is a remarkable difference between the two cases. It is already known from the i.i.d. case that in the first situation the full \(\sqrt n\)-consistency is not attainable. On the contrary to this for continuous time processes the authors prove a limit theorem at full rate \(\sqrt T\) under weak mixing assumptions and weak conditions imposed on the two-dimensional densities of the process.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 62G05
zbMATH DE Number: 1271182
zbMATH Keywords: central limit theorem
zbMATH Keywords: mixing sequences
zbMATH Keywords: density kernel estimator
MaRDI profile type: Publication
full work available at URL: jmva.1998.1785
OpenAlex ID: W1993986196
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DOI: 10.1006/JMVA.1998.1785
description: scientific article; zbMATH DE number 1271182