OJS  Vol.3 No.3 , June 2013
Strong Consistency of Kernel Regression Estimate
Abstract: In this paper, regression function estimation from independent and identically distributed data is considered. We establish strong pointwise consistency of the famous Nadaraya-Watson estimator under weaker conditions which permit to apply kernels with unbounded support and even not integrable ones and provide a general approach for constructing strongly consistent kernel estimates of regression functions.
Cite this paper: W. Cui and M. Wei, "Strong Consistency of Kernel Regression Estimate," Open Journal of Statistics, Vol. 3 No. 3, 2013, pp. 179-182. doi: 10.4236/ojs.2013.33020.

[1]   E. A. Nadaraya, “On Estimating Regression,” Theory of Probability and Its Applications, Vol. 9, No. 1, 1964, pp. 141-142. doi:10.1137/1109020

[2]   G. S. Watson, “Smooth Regression Analysis,” Sankhya: The Indian Journal of Statistics, Series A, Vol. 26, No. 4, 1964, pp. 359-372.

[3]   C. J. Stone, “Consistent Nonparametric Regression,” Annals of Statistics, Vol. 5, No. 4, 1977, pp. 595-620. doi:10.1214/aos/1176343886

[4]   E. F. Schuster and S. Yakowitz, “Contributions to the Theory of Nonparametric Regression, with Application to System Identification,” Annals Statistics, Vol. 7, No. 1, 1979, pp. 139-149. doi:10.1214/aos/1176344560

[5]   T. Gasser and H. G. Müller, “Estimating Regression Functions and Their Derivatives by the Kernel Method,” Scandinavian Journal of Statistics, Vol. 11, 1984, pp. 171-185.

[6]   Y. P. Mack and H. G. Müller, “Derivative Estimation in Nonparametric Regression with Random Predictor,” Sankhya: The Indian Journal of Statistics (Series A), Vol. 51, No. 1, 1989, pp. 59-72.

[7]   W. Greblicki and M. Pawlak, “Cascade Non-Linear System Identification by a Non-Parametric Method,” International Journal of Systems Science, Vol. 25, No. 1, 1994, 129-153. doi:10.1080/00207729408928949

[8]   M. Kohler, A. Krzy?ak and H. Walk, “Strong Consisten cy of Automatic Kernel Regression Estimates,” Annals of the Institute of Statistical Mathematics, Vol. 55, No. 2, 2003, pp. 287-308.

[9]   M. Kohler, A. Krzy?ak and H. Walk, “Rates of Convergence for Partition-Zing and Nearest Neighbor Regression Estimates with Unbounded Data,” Journal of Multivariate Analysis, Vol. 97, No. 2, 2006, pp. 311-323. doi:10.1016/j.jmva.2005.03.006

[10]   H. Walk, “Strong Universal Consistency of Smooth Kernel Regression Estimates,” Annals of the Institute of Statistical Mathematics, Vol. 57, No. 4, 2005, pp. 665-685. doi:10.1007/BF02915432

[11]   L. Devroye, “On the Almost Everywhere Convergence of Nonparametric Regression Function Estimates,” Annals Statistics, Vol. 9, No. 6, 1981, pp. 1310-1319. doi:10.1214/aos/1176345647

[12]   L. C. Zhao and Z. B. Fang, “Strong Convergence of Kernel Estimates of Nonparametric Regression Functions,” Chinese Annals of Mathematics, Series B, Vol. 6, No. 2, 1985, pp. 147-155.

[13]   W. Greblicki, A. Krzyzak and M. Pawlak, “Distribution Free Pointwise Consistency of Kernel Regression Estimate,” Annals Statistics, Vol. 12, No. 4, 1984, pp. 1570-1575. doi:10.1214/aos/1176346815