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Kernel density estimation for linear processes: Asymptotic normality and optimal bandwidth derivation |
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| Authors: | Marc Hallin Lanh Tat Tran |
| Institution: | (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, 47405-5701 Bloomington, IN, U.S.A. |
| 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.Supported in part by NSF grant DMS-9403718. |
| Keywords: | Density estimation linear process kernel bandwidth mean square error |
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