On central and non-central limit theorems in density estimation for sequences of long-range dependence
type: Item
instance of: scholarly article
title: On central and non-central limit theorems in density estimation for sequences of long-range dependence
zbMATH Open document ID: 0902.62046
DOI: 10.1016/0304-4149(96)00072-5
author: Hwai-Chung Ho
published in: Stochastic Processes and their Applications
publication date: 1998-11-23T00:00:00Z
review text: The paper studies the asymptotic properties of kernel density estimators of stationary sequences which are observed through some non-linear instantaneous filter applied to long-range dependent Gaussian sequences [see \textit{J. Beran}, Statistical methods for data with long-range dependence. Stat. Sci. 7, 404-427 (1992)]. In the three main theorems, the author shows that under long-range dependence the limiting distribution of the kernel estimator can be Gaussian or non-Gaussian depending on the choice of the bandwidth sequences. The theorems also contain some interesting properties which contrast noticeably to the short-range-dependent cases. In particular, if the bandwith \(h(N)\) for samples of size \(N\) is selected to converge to zero fast enough, the usual \(\sqrt {Nh(N)}\)-rate asymptotic normality still holds.
Mathematics Subject Classification ID: 62G07
Mathematics Subject Classification ID: 62G20
Mathematics Subject Classification ID: 60G10
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 1226247
zbMATH Keywords: long-range dependence
zbMATH Keywords: central limit theorems
zbMATH Keywords: kernel density estimator
zbMATH Keywords: instantaneous filter
reviewed by: Gejza Dohnal
MaRDI profile type: Publication
full work available at URL: 0304-4149(96)00072-5
OpenAlex ID: W1975234525
cites work: Q5560061
cites work: On smoothed probability density estimation for stationary processes
cites work: Density estimation for linear processes
cites work: Q4839936
cites work: The empirical process of some long-range dependent sequences with an application to U-statistics
cites work: Non-central limit theorems for non-linear functional of Gaussian fields
cites work: Q5624436
cites work: Nonparametric curve estimation from time series
cites work: Efficiency of a Kernel Density Estimator Under an Autoregressive Dependence Model
cites work: Convergence rates in density estimation for data from infinite-order moving average processes
cites work: Q5598785
cites work: Multiple Wiener-Ito integrals. With applications to limit theorems
cites work: NONPARAMETRIC ESTIMATORS FOR TIME SERIES
cites work: Q4015742
cites work: Q3290160
cites work: Q3634329
cites work: Nonparametric estimation in Markov processes
cites work: Q4727203
cites work: Law of the iterated logarithm for sums of non-linear functions of Gaussian variables that exhibit a long range dependence
cites work: Convergence of integrated processes of arbitrary Hermite rank
description: scientific article; zbMATH DE number 1226247