Global convergence of the recursive kernel regression estimates with applications in classification and nonlinear system estimation

Author

Krzyzak, Adam

Author_Institution

Dept. of Comput. Sci., Concordia Univ., Montreal, Que., Canada

Volume

38

Issue

4

fYear

1992

fDate

7/1/1992 12:00:00 AM

Firstpage

1323

Lastpage

1338

Abstract

An improved exponential bound on the L₁ error for the recursive kernel regression estimates is derived. It is shown, using the martingale device, that weak, strong and complete L ₁ consistencies are equivalent. Consequently the conditions on a certain smoothing sequence are necessary and sufficient for strong L₁ consistency of the recursive kernel regression estimate. The rates of global convergence are also given. Obtained results are applied to recursive classification rules and to nonlinear time series estimation

Keywords

convergence; estimation theory; information theory; nonlinear systems; recursive functions; statistical analysis; time series; L₁ error; classification; exponential bound; global convergence; martingale device; nonlinear system estimation; nonlinear time series estimation; recursive kernel regression estimates; smoothing sequence; Chaos; Computer science; Control theory; Convergence; Information theory; Kernel; Nonlinear systems; Parametric statistics; Recursive estimation; Smoothing methods;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.144711

Filename

144711