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

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  • Einmahl, J.H.J.

    (Tilburg University, School of Economics and Management)

Abstract

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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Suggested Citation

  • Einmahl, J.H.J., 1989. "Limit theorems for the negative parts of weighted multivariate empirical processes with application," Other publications TiSEM d54f2928-e48e-40bb-8959-5, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:d54f2928-e48e-40bb-8959-57b3666a8893
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