Strong consistency of regression function estimates

Zhang Shuang Lin

Kybernetika (1995)

  • Volume: 31, Issue: 4, page 375-384
  • ISSN: 0023-5954

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Lin, Zhang Shuang. "Strong consistency of regression function estimates." Kybernetika 31.4 (1995): 375-384. <http://eudml.org/doc/27829>.

@article{Lin1995,
author = {Lin, Zhang Shuang},
journal = {Kybernetika},
keywords = {strong consistency; nonparametric regression; partitioning estimate; kernel estimate},
language = {eng},
number = {4},
pages = {375-384},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Strong consistency of regression function estimates},
url = {http://eudml.org/doc/27829},
volume = {31},
year = {1995},
}

TY - JOUR
AU - Lin, Zhang Shuang
TI - Strong consistency of regression function estimates
JO - Kybernetika
PY - 1995
PB - Institute of Information Theory and Automation AS CR
VL - 31
IS - 4
SP - 375
EP - 384
LA - eng
KW - strong consistency; nonparametric regression; partitioning estimate; kernel estimate
UR - http://eudml.org/doc/27829
ER -

References

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  1. J. Beck, The exponential rate of convergence of error for k n NN nonparametric regression and decision, Problems Control Inform. Theory 8 (1979), 303-311. (1979) 
  2. G. Collomb, Nonparametric regression: an up-to-date bibliography, Statistics 16 (1985), 300-324. (1985) Zbl0574.62043
  3. H. Chernoff, A measure of asymptotic efficiency of tests of a hypothesis based on the sum of observations, Ann. Math. Statist. 25 (1952), 493-507. (1952) MR0057518
  4. L. Devroye, Necessary and sufficient conditions for the almost everywhere convergence of nearest neighbor regression function estimates, Z. Wahrsch. verw. Geb. 61 (1982), 467-481. (1982) MR0682574
  5. L. Devroye, L. Gyorfi, Distribution-free exponential bound on the L 1 error of partitioning estimates of a regression function, In: Proceedings of the Fourth Pannonian Symposium on Mathematical Statistics (F. Konecny, J. Mogyorodi, W. Wertz, eds.), Akademiai Kiado, Budapest 1983, pp. 67-76. (1983) MR0851019
  6. L. Devroye L. Gyorfi G. Lugosi, A. Krzyzak, On strong universal consistency of nearest neighbor regression function estimates, Ann. Statist. To appear. MR1311980
  7. L. Devroye, A. Krzyzak, An equivalence theorem for L 1 convergence of the kernel regression estimate, J. Statist. Plann. Inference 23 (1989), 71-82. (1989) MR1029241
  8. L. Devroye, T.J. Wagner, Distribution-free consistency results in nonparametric discrimination and regression function estimation, Ann. Statist. 8 (1980), 231-239. (1980) Zbl0431.62025MR0560725
  9. M. Falk, R. D. Reiss, A Hellinger distance bound for the nearest neighbor approach in conditional curve estimation, Statist. Decisions, Supplement Issue 3 (1993), 55-68. (1993) Zbl0795.62035MR1244063
  10. L. Gyorfi, Universal consistencies of a regression estimate for unbounded regression functions, In: Nonparametric Functional Estimation (G. Roussas, ed.), NATO ASI Series, Springer-Verlag, Berlin 1991, pp. 329-338. (1991) MR1154338
  11. E. A. Nadaraya, On estimating regression, Theory Probab. Appl. 5 (1964), 141-142. (1964) Zbl0136.40902
  12. C. Spiegelman, J. Sacks, Consistent window estimation in nonparametric regression, Ann. Statist. 8 (1980), 240-246. (1980) Zbl0432.62066MR0560726
  13. C. J. Stone, Consistent nonparametric regression, Ann. Statist. 8 (1977), 1348-1360. (1977) Zbl0366.62051MR0594650
  14. G. S. Watson, Smooth regression analysis, Sankhya. Ser. A 26 (1964), 359-372. (1964) Zbl0137.13002MR0185765
  15. L. C. Zhao, Exponential bounds of mean error for the nearest neighbor estimates of regression functions, J. Multivariate Anal. 21 (1987), 168-178. (1987) Zbl0622.62044MR0877849

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