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KERNEL DENSITY ESTIMATION FOR LINEAR PROCESSES:

ASYMPTOTIC NORMALITY AND

OPTIMAL BANDWIDTH DERIVATION

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MARC HALLIN^{1} AND LANH
TAT TRAN^{2}

^{1} *Institut de Statistique, Université Libre de Bruxelles,
Campus de la Plaine CP 210,*

Boulevard du Triomphe, B-1050 Bruxelles, Belgium

^{2} *Department of Mathematics, College of Arts and Sciences,
Indiana University,*

Rawles Hall, Bloomington, IN 47405-5701, U.S.A.
(Received January 4, 1994; revised September 21, 1995)

**Abstract.**
The problem of estimating the marginal density
of a linear process by kernel methods is considered. Under general
conditions, kernel density estimators are shown to be asymptotically
normal. Their limiting covariance matrix is computed. We also find
the optimal bandwidth in the sense that it asymptotically minimizes
the mean square error of the estimators. The assumptions involved
are easily verifiable.

*Key words and phrases*:
Density estimation, linear
process, kernel, bandwidth, mean square error.

**Source**
( TeX ,
DVI ,
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