Optimal global rates of convergence for nonparametric regression with unbounded data

Journal of Statistical Planning and Inference

Volumn 139, Issue 4, 2009, Pages 1286-1296

  Kohler, Michael ^a   Krzyzak, Adam ^b   Walk, Harro ^c  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

^b Gina Cody School of Engineering and Computer Science   (Canada)

^c UNIVERSITY OF STUTTGART   (Germany)

Author keywords

Kernel estimate; Rate of convergence; Regression

Indexed keywords

EID: 57749209659     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2008.07.012     Document Type: Article

References (24)

1. Cover, T.M., 1968. Rates of convergence for nearest neighbor procedures. Proceedings of the Hawaii International Conference on System Sciences, Honolulu, HI, pp. 413-415.
2. Devroye L. Any discrimination rule can have arbitrarily bad probability of error for finite sample size. IEEE Trans. Pattern Anal. Mach. Intell. 4 (1982) 154-157
3. 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
4. Greblicki W., Krzyżak A., and Pawlak M. Distribution-free pointwise consistency of kernel regression estimate. Ann. Statist. 12 (1984) 1570-1575
5. n-NN regression estimates and classification rules. IEEE Trans. Inform. Theory 27 (1981) 362-364
6. Györfi L., and Walk H. On the strong universal consistency of a series type regression estimate. Math. Methods Statist. 5 (1996) 332-342
7. Györfi L., and Walk H. On the strong universal consistency of a recursive regression estimate by Pál Révész. Statist. Probab. Lett. 31 (1997) 177-183
8. Györfi L., Kohler M., and Walk H. Weak and strong universal consistency of semi-recursive partitioning and kernel regression estimates. Statist. Decisions 16 (1998) 1-18
9. Györfi L., Kohler M., Krzyżak A., and Walk H. A Distribution-Free Theory of Nonparametric Regression. Springer Series in Statistics (2002), Springer, New York
10. Kohler M. Universally consistent regression function estimation using hierarchical B-splines. J. Multivariate Anal. 67 (1999) 138-164
11. Kohler M. Inequalities for uniform deviations of averages from expectations with applications to nonparametric regression. J. Statist. Plann. Inference 89 (2000) 1-23
12. Kohler M. Universal consistency of local polynomial kernel regression estimates. Ann. Inst. Statist. Math. 54 (2002) 879-899
13. Kohler M. Nonparametric regression with additional measurement errors in the dependent variable. J. Statist. Plann. Inference 136 (2006) 3339-3361
14. Kohler M., and Krzyżak A. Nonparametric regression estimation using penalized least squares. IEEE Trans. Inform. Theory 47 (2001) 3054-3058
15. Kohler M., Krzyżak A., and Walk H. Rates of convergence for partitioning and nearest neighbor regression estimates with unbounded data. J. Multivariate Anal. 97 (2006) 311-323
16. Kulkarni S.R., and Posner S.E. Rates of convergence of nearest neighbor estimation under arbitrary sampling. IEEE Trans. Inform. Theory 41 (1995) 1028-1039
17. Liitiäinen, E., Corona, F., Lendasse, A., 2007. Nearest neighbor distributions and noise variance estimation. ESANN'2007 Proceedings-European Symposium on Artificial Neural Networks, Bruge, Belgium, pp. 67-72.
18. Lugosi G., and Zeger K. Nonparametric estimation via empirical risk minimization. IEEE Trans. Inform. Theory 41 (1995) 677-687
19. Nobel A. Histogram regression estimation using data-dependent partitions. Ann. Statist. 24 (1996) 1084-1105
20. Spiegelman C., and Sacks J. Consistent window estimation in nonparametric regression. Ann. Statist. 8 (1980) 240-246
21. Stone C.J. Consistent nonparametric regression. Ann. Statist. 5 (1977) 595-645
22. Stone C.J. Optimal global rates of convergence for nonparametric regression. Ann. Statist. 10 (1982) 1040-1053
23. Walk H. Strong universal consistency of smooth kernel regression estimates. Ann. Inst. Statist. Math. 57 (2005) 665-685
24. Walk H. A universal strong law of large numbers for conditional expectations via nearest neighbors. J. Multivariate Anal. 99 (2008) 1035-1050