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Strong Universal Pointwise Consistency of Some Regression Function Estimates

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  • Algoet, Paul
  • Györfi, László

Abstract

The strong universal pointwise consistency of some modified versions of the standard regression function estimates of partitioning, kernel, and nearest neighbor type is shown.

Suggested Citation

  • Algoet, Paul & Györfi, László, 1999. "Strong Universal Pointwise Consistency of Some Regression Function Estimates," Journal of Multivariate Analysis, Elsevier, vol. 71(1), pages 125-144, October.
    • Handle: RePEc:eee:jmvana:v:71:y:1999:i:1:p:125-144
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    References listed on IDEAS

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    1. Yakowitz, Sid, 1993. "Nearest neighbor regression estimation for null-recurrent Markov time series," Stochastic Processes and their Applications, Elsevier, vol. 48(2), pages 311-318, November.
    2. Devroye, Luc & Wise, Gary L., 1980. "Consistency of a recursive nearest neighbor regression function estimate," Journal of Multivariate Analysis, Elsevier, vol. 10(4), pages 539-550, December.
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    Cited by:

    1. Matthias Hansmann & Benjamin M. Horn & Michael Kohler & Stefan Ulbrich, 2022. "Estimation of conditional distribution functions from data with additional errors applied to shape optimization," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(3), pages 323-343, April.
    2. Walk, Harro, 2008. "A universal strong law of large numbers for conditional expectations via nearest neighbors," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1035-1050, July.
    3. Nengxiang Ling & Shuhe Hu, 2008. "Asymptotic distribution of partitioning estimation and modified partitioning estimation for regression functions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(4), pages 353-363.
    4. Kohler, Michael & Krzyzak, Adam, 2007. "Asymptotic confidence intervals for Poisson regression," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 1072-1094, May.
    5. Harro Walk, 2001. "Strong Universal Pointwise Consistency of Recursive Regression Estimates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(4), pages 691-707, December.

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