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Gaussian approximation of local empirical processes indexed by functions
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  • Published: March 1997

Gaussian approximation of local empirical processes indexed by functions

  • Uwe Einmahl1 &
  • David M. Mason2 

Probability Theory and Related Fields volume 107, pages 283–311 (1997)Cite this article

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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.

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Authors and Affiliations

  1. Department of Mathematics, Indiana University, Bloomington, IN 47405, USA , , , , , , IN

    Uwe Einmahl

  2. Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA (e-mail: davidm@ brahms.udel.edu), , , , , , US

    David M. Mason

Authors
  1. Uwe Einmahl
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  2. David M. Mason
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Additional information

Received: 11 January 1995/In revised form: 12 July 1996

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Einmahl, U., Mason, D. Gaussian approximation of local empirical processes indexed by functions. Probab Theory Relat Fields 107, 283–311 (1997). https://doi.org/10.1007/s004400050086

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  • Issue Date: March 1997

  • DOI: https://doi.org/10.1007/s004400050086

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  • Mathematics Subject Classification (1991): 60F15
  • 62G05
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