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June, 1995 Density Estimation Under Long-Range Dependence
Sandor Csorgo, Jan Mielniczuk
Ann. Statist. 23(3): 990-999 (June, 1995). DOI: 10.1214/aos/1176324632

Abstract

Dehling and Taqqu established the weak convergence of the empirical process for a long-range dependent stationary sequence under Gaussian subordination. We show that the corresponding density process, based on kernel estimators of the marginal density, converges weakly with the same normalization to the derivative of their limiting process. The phenomenon, which carries on for higher derivatives and for functional laws of the iterated logarithm, is in contrast with independent or weakly dependent situations, where the density process cannot be tight in the usual function spaces with supremum distances.

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Sandor Csorgo. Jan Mielniczuk. "Density Estimation Under Long-Range Dependence." Ann. Statist. 23 (3) 990 - 999, June, 1995. https://doi.org/10.1214/aos/1176324632

Information

Published: June, 1995
First available in Project Euclid: 11 April 2007

zbMATH: 0843.62037
MathSciNet: MR1345210
Digital Object Identifier: 10.1214/aos/1176324632

Subjects:
Primary: 62G07
Secondary: 60F17, 62M99

Rights: Copyright © 1995 Institute of Mathematical Statistics

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Vol.23 • No. 3 • June, 1995
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