Global Convergence Of The Recursive Kernel Regression Estimates With Applications In Classification And Nonlinear System Estimation英文电子书.pdf

IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 38, NO. 4, JULY 1992 1323 Global Convergence of the Recursive Kernel Regression Estimates with Applications in Classification and Nonlinear System Estimation Adam Krzyzak, Member, IEEE Abstract-An improved exponential bound on the L , error arbitrary distribution and distribution-free convergence re- for the recursive kernel regression estimates is derived. It is sults are available, that is convergence can be obtained for all shown, using the martingale device, that weak, strong and input distributions and for all nonlinear regressions. Distribu- complete L , consistencies are equivalent. Consequently the con- ditions on the smoothing sequence c:=,hf+ 00 and tion-free results are the most natural results in the context of ~ ~ = l h ~ ~ ~ h . , r Jas/ ~n -+j n03= forI h all~ e o are necessary nonparametric estimation, since we would like the estimates and sufficiknt for strong L , consistency of the recursive kernel to extract all statistical information from the observations regression estimate. The rates of global convergence are also only without presupposing anything about the reality. From given. Obtained results are applied to recursive classification rules and to nonlinear time series estimation. now on, we focus our attention on random design approach. Distribution-free pointwise convergence of the k