Limit theorems for the negative parts of weighted multivariate empirical processes with application
AbstractNecessary and sufficient conditions for weak convergence and strong (functional) limit theorems for the negative parts of weighted multivariate empirical processes are obtained. These results are considerably different from those for the positive parts (or absolute values) of these processes. Moreover, a short proof of Kiefer's (1961, Pacific J. Math. 11, 649-660) exponential inequality for the Kolmogorov-Smirnov statistic of the multivariate empirical process is presented. Also an application of one of the main results to strong limit theorems for the ratio of the true to the empirical distribution function is included.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Multivariate Analysis.
Volume (Year): 29 (1989)
Issue (Month): 2 (May)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
Other versions of this item:
- Einmahl, J.H.J., 1989. "Limit theorems for the negative parts of weighted multivariate empirical processes with application," Open Access publications from Tilburg University urn:nbn:nl:ui:12-142052, Tilburg University.
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