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Limit theorems for the negative parts of weighted multivariate empirical processes with application


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  • Einmahl, John H. J.


Necessary 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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Article provided by Elsevier in its journal Journal of Multivariate Analysis.

Volume (Year): 29 (1989)
Issue (Month): 2 (May)
Pages: 199-218

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Handle: RePEc:eee:jmvana:v:29:y:1989:i:2:p:199-218

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Keywords: exponential inequality negative part of empirical process strong limit theorems weak convergence weight functions;

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