Gaussian approximation of local empirical processes indexed by functions |
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Authors: | Uwe Einmahl David M. Mason |
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Affiliation: | (1) Department of Mathematics, Indiana University, Bloomington, IN 47405, USA , IN;(2) Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA (e-mail: davidm@ brahms.udel.edu), US |
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Abstract: | Summary. An extended notion of a local empirical process indexed by functions is introduced, which includes kernel density and regression function estimators and the conditional empirical process as special cases. Under suitable regularity conditions a central limit theorem and a strong approximation by a sequence of Gaussian processes are established for such processes. A compact law of the iterated logarithm (LIL) is then inferred from the corresponding LIL for the approximating sequence of Gaussian processes. A number of statistical applications of our results are indicated. Received: 11 January 1995/In revised form: 12 July 1996 |
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Keywords: | Mathematics Subject Classification (1991): 60F15 62G05 |
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