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

Journal of Multivariate Analysis

Volumn 99, Issue 6, 2008, Pages 1035-1050

  Walk, Harro ^a  

^a UNIVERSITY OF STUTTGART   (Germany)

Author keywords

Conditional expectation; Nearest neighbor regression estimation; Strong law of large numbers; Strong universal pointwise consistency

Indexed keywords

EID: 43049124467     PISSN: 0047259X     EISSN: 10957243     Source Type: Journal    
DOI: 10.1016/j.jmva.2007.06.009     Document Type: Article

References (18)

1. Algoet P. Universal schemes for learning the best nonlinear predictor given the infinite past and side information. IEEE Trans. Inform. Theory 45 (1999) 1165-1185
2. Algoet P., and Györfi L. Strong universal pointwise consistency of some regression function estimation. J. Multivariate Anal. 71 (1999) 125-144
3. Devroye L. On the almost everywhere convergence of nonparametric function estimates. Ann. Statist. 9 (1981) 1310-1319
4. Devroye L., Györfi L., Krzyżak A., and Lugosi G. On the strong universal consistency of nearest neighbor regression function estimates. Ann. Statist. 22 (1994) 1371-1385
5. Devroye L., Györfi L., and Lugosi G. A Probabilistic Theory of Pattern Recognition (1996), Springer, New York
6. Efron B., and Stein C. The jackknife estimate of variance. Ann. Statist. 9 (1981) 586-596
7. Etemadi N. An elementary proof of the strong law of large numbers, Z. Wahrscheinlichkeitstheorie verw. Gebiete 55 (1981) 119-122
8. W. Feller, An Introduction to Probability Theory and its Applications, second ed., vol. II, Wiley, New York, 1971.
9. Greblicki W., Krzyżak A., and Pawlak M. Distribution-free pointwise consistency of kernel regression estimate. Ann. Statist. 12 (1984) 1570-1575
10. Györfi L., Kohler M., Krzyżak A., and Walk H. A Distribution-Free Theory of Nonparametric Regression (2002), Springer, New York
11. Kozek A.S., Leslie J.R., and Schuster E.F. On a universal strong law of large numbers for conditional expectations. Bernoulli 4 (1998) 143-165
12. Mukerjee H. A strong law of large numbers for nonparametric regression. J. Multivariate Anal. 30 (1989) 17-26
13. Steele J.M. An Efron-Stein inequality for nonsymmetric statistics. Ann. Statist. 14 (1986) 753-758
14. Stone C.J. Consistent nonparametric regression. Ann. Statist. 5 (1977) 595-645
15. Stute W. On almost sure convergence of conditional empirical distribution functions. Ann. Probab. 14 (1986) 891-901
16. Walk H. Strong universal pointwise consistency of recursive regression estimates. Ann. Inst. Statist. Math. 53 (2001) 691-707
17. Wheeden R.L., and Zygmund A. Measure and Integral (1977), Marcel Dekker, New York
18. Zhao L.C., and Fang Z.B. Strong convergence of kernel estimates of nonparametric regression functions. Chinese Ann. Math. Ser. B 6 (1985) 147-155