Asymptotic properties of density estimates for linear processes: application of projection method

Authors: Artur Bryk; Jan Mielniczuk

Source: Journal of Nonparametric Statistics, Volume 17, Number 1, January-February 2005 , pp. 121-133(13)

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Abstract:

We specify conditions under which kernel density estimate for linear process is weakly and strongly consistent, and establish rates of its pointwise and uniform convergence. In particular, it is proved that for short-range dependent data of size n and bandwidth b n , the rate of convergence is . The results are established using projection method introduced in this setup by Ho and Hsing (Ho, H. C. and Hsing, T. (1996). On asymptotic expansion of the empirical process of long-memory moving averages. Annals of Statistics , 24 , 992-1024.) and Wu (Wu, W. B. (2001). Nonparametric estimation for stationary processes, Ph.D. thesis , University of Michigan, available at http://www.stat.uchicago.edu/research/techreports.html.). ¶ Affiliated also with Polish-Japanese Institute of Information Technology, Warsaw, Poland

Keywords: Long- and short-range dependence; Kernel density estimators; Linear process; Projection method; Rates of convergence

Document Type: Research article

DOI: http://dx.doi.org/10.1080/10488525042000267770

Affiliations: 1: Institute of Computer Science, Polish Academy of Sciences Ordona 21 01-237 Warsaw Poland

Publication date: 2005-01-01