Limit theorems for the negative parts of weighted multivariate empirical processes with application
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.
Year of publication: |
1989
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Authors: | Einmahl, John H. J. |
Published in: |
Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 29.1989, 2, p. 199-218
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Publisher: |
Elsevier |
Keywords: | exponential inequality negative part of empirical process strong limit theorems weak convergence weight functions |
Saved in:
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