The Annals of Statistics

Kernel density estimation for linear processes

Jan Mielniczuk and Wei Biao Wu

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Abstract

In this paper we provide a detailed characterization of the asymptotic behavior of kernel density estimators for one-sided linear processes. The conjecture that asymptotic normality for the kernel density estimator holds under short-range dependence is proved under minimal assumptions on bandwidths. We also depict the dichotomous and trichotomous phenomena for various choices of bandwidths when the process is long-range dependent.

Article information

Source
Ann. Statist., Volume 30, Number 5 (2002), 1441-1459.

Dates
First available in Project Euclid: 28 October 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1035844982

Digital Object Identifier
doi:10.1214/aos/1035844982

Mathematical Reviews number (MathSciNet)
MR1936325

Zentralblatt MATH identifier
1015.62034

Subjects
Primary: 62F05: Asymptotic properties of tests 60F17: Functional limit theorems; invariance principles
Secondary: 60G35: Signal detection and filtering [See also 62M20, 93E10, 93E11, 94Axx]

Keywords
Long- and short-range dependence kernel density estimators linear process martingale central limit theorem

Citation

Wu, Wei Biao; Mielniczuk, Jan. Kernel density estimation for linear processes. Ann. Statist. 30 (2002), no. 5, 1441--1459. doi:10.1214/aos/1035844982. https://projecteuclid.org/euclid.aos/1035844982


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  • CHICAGO, ILLINOIS 60637 E-MAIL: wbwu@galton.uchicago.edu INSTITUTE OF COMPUTER SCIENCE POLISH ACADEMY OF SCIENCES ORDONA 21 01-237 WARSAW POLAND E-MAIL: miel@ipipan.waw.pl