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Conditional empirical processes

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Seminar on Empirical Processes

Part of the book series: DMV Seminar ((OWS,volume 9))

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Abstract

Consider a sequence ξi=(Xi,Yi), i≥1, of independent ℝd+1 random vectors with common d.f.H:

$${\text{H}}\left( {{\text{x,y}}} \right) = \mathbb{P}\left( {{\text{X < x,Y < y}}} \right),{\text{ }}\left( {{\text{x, y}}} \right) \in {\mathbb{R}^{{\text{d + 1}}}}$$

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References (and further reading)

  • Billingsley, P. (1968), Convergence of probability measures. New York: Wiley.

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  • Stute, W. (1986). Conditional empirical processes. Ann. Statist. 14, 638–647.

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  • Stute, W. (1986). On almost sure convergence of conditional empirical distribution functions. Ann. Prob. 14, 891–901.

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  • Yang, S.S. (1981). Linear functions of concomitants of order statistics with applications to nonparametrie estimation of a regression function. J. Amer. Statist. Assoc. 76, 658–662.

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Author information

Authors and Affiliations

  1. Mathematisches Institut, Universität München, Theresienstrasse 39, D-8000, München 2, Germany

    Peter Gaenssler

  2. Mathematisches Institut, Universität Giessen, Arndstrasse 2, D-6300, Giessen, Germany

    Winfried Stute

Authors
  1. Peter Gaenssler
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  2. Winfried Stute
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© 1987 Springer Basel AG

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Gaenssler, P., Stute, W. (1987). Conditional empirical processes. In: Seminar on Empirical Processes. DMV Seminar, vol 9. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6269-1_4

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  • DOI: https://doi.org/10.1007/978-3-0348-6269-1_4

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-7643-1921-2

  • Online ISBN: 978-3-0348-6269-1

  • eBook Packages: Springer Book Archive

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