A note on L1 density estimation for linear processes

Somnath Datta

Journal of Time Series Analysis, 1997, vol. 18, issue 4, 375-383

Abstract: In this paper, we consider the L1 performance of a kernel estimator, f^n of the density of a linear process Xt∑∞k=0akZt−k, a0 = 1, where {Zt} is a sequence of independent and identically distributed (i.i.d.) random variables with E|Z1|ε 1, and {ak} is a sequence of reals converging to zero at a certain rate. Asymptotic minimizations of the integrated L1 risk of fn 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 L1 View. New York: Wiley, 1985) and by Hall and Wand (Minimizing the L1 distance in nonparametric density estimation, J. Multivariate Anal.26 (1988), 59–88) to the linear process case. Numerical examples to illustrate the performance of fn are also presented.

Date: 1997
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