A note on  L  1  density estimation for linear processes | Zendy

Datta Somnath | Zendy

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A note on L 1 density estimation for linear processes

Author(s) -

Datta Somnath

Publication year - 1997

Publication title -

journal of time series analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.576

H-Index - 54

eISSN - 1467-9892

pISSN - 0143-9782

DOI - 10.1111/1467-9892.00056

Subject(s) - mathematics , estimator , independent and identically distributed random variables , kernel density estimation , sequence (biology) , zero (linguistics) , nonparametric statistics , random variable , kernel (algebra) , density estimation , combinatorics , multivariate kernel density estimation , multivariate statistics , statistics , discrete mathematics , variable kernel density estimation , kernel method , linguistics , philosophy , artificial intelligence , biology , computer science , support vector machine , genetics

In this paper, we consider the L 1 performance of a kernel estimator, f^ n of the density of a linear process X t ∑ ∞ k =0 a k Z t−k , a 0 = 1, where { Z t } is a sequence of independent and identically distributed (i.i.d.) random variables with E | Z 1 | ε < ∞, for some ε > 1, and { a k } is a sequence of reals converging to zero at a certain rate. Asymptotic minimizations of the integrated L 1 risk of f n and its upper bounds are considered. This paper extends the earlier results for the i.i.d. case by Devroye and Gyorfi ( Nonparametric Density Estimation: The L 1 View. New York: Wiley, 1985) and by Hall and Wand (Minimizing the L 1 distance in nonparametric density estimation, J. Multivariate Anal. 26 (1988), 59–88) to the linear process case. Numerical examples to illustrate the performance of f n are also presented.

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