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A universal strong law of large numbers for conditional expectations via nearest neighbors

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  • Walk, Harro

Abstract

For kn-nearest neighbor estimates of a regression Y on X (d-dimensional random vector X, integrable real random variable Y) based on observed independent copies of (X,Y), strong universal pointwise consistency is shown, i.e., strong consistency PX-almost everywhere for general distribution of (X,Y). With tie-breaking by indices, this means validity of a universal strong law of large numbers for conditional expectations E(YX=x).

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:99:y:2008:i:6:p:1035-1050
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    References listed on IDEAS

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    1. Mukerjee, Hari, 1989. "A strong law of large numbers for nonparametric regression," Journal of Multivariate Analysis, Elsevier, vol. 30(1), pages 17-26, July.
    2. 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.
    3. 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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    Cited by:

    1. Christoph March, 2011. "Adaptive social learning," PSE Working Papers halshs-00572528, HAL.
    2. Jules L. Ellis & Klaas Sijtsma, 2024. "Proof of Reliability Convergence to 1 at Rate of Spearman–Brown Formula for Random Test Forms and Irrespective of Item Pool Dimensionality," Psychometrika, Springer;The Psychometric Society, vol. 89(3), pages 774-795, September.
    3. Matthias Hansmann & Michael Kohler & Harro Walk, 2019. "On the strong universal consistency of local averaging regression estimates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1233-1263, October.

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