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Central limit theorem for the empirical process

Giraitis, Liudas and Surgailis, Donatas (1999) Central limit theorem for the empirical process. Journal of Statistical Planning and Inference, 80 (1-2). pp. 81-93. ISSN 0378-3758

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Abstract

We discuss the functional central limit theorem (FCLT) for the empirical process of a moving-average stationary sequence with long memory. The cases of one-sided and double-sided moving averages are discussed. In the case of one-sided (causal) moving average, the FCLT is obtained under weak conditions of smoothness of the distribution and the existence of (2+δ)-moment of i.i.d. innovations, by using the martingale difference decomposition due to Ho and Hsing (1996, Ann. Statist. 24, 992–1014). In the case of double-sided moving average, the proof of the FCLT is based on an asymptotic expansion of the bivariate probability density.

Item Type: Article
Official URL: http://www.sciencedirect.com/science/journal/03783...
Additional Information: © 1999 Elsevier Science B.V.
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 19 Feb 2010 10:40
URL: http://eprints.lse.ac.uk/7164/

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