Local generalized empirical estimation of regression |
| |
Authors: | Email author" target="_blank">Jiancheng?JiangEmail author Kjell?Doksum |
| |
Institution: | 1. LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China 2. Department of Statistics, University of California at Berkeley, CA 94720, USA |
| |
Abstract: | Letf(x) be the density of a design variableX andm(x) = EY∣X = x] the regression function. Thenm(x) = G(x)/f(x), whereG(x) = rn(x)f(x). The Dirac δ-function is used to define a generalized empirical functionG
n(x) forG(x) whose expectation equalsG(x). This generalized empirical function exists only in the space of Schwartz distributions, so we introduce a local polynomial
of orderp approximation toG
n(.) which provides estimators of the functionG(x) and its derivatives. The densityf(x) can be estimated in a similar manner. The resulting local generalized empirical estimator (LGE ) ofm(x) is exactly the Nadaraya-Watson estimator at interior points whenp = 1, but on the boundary the estimator automatically corrects the boundary effect. Asymptotic normality of the estimator
is established. Asymptotic expressions for the mean squared errors are obtained and used in bandwidth selection. Boundary
behavior of the estimators is investigated in details. We use Monte Carlo simulations to show that the proposed estimator
withp = 1 compares favorably with the Nadaraya-Watson and the popular local linear regression smoother. |
| |
Keywords: | boundary adaptive Dirac δ-function local polynomial local empirical Nadaraya-Watson estimator |
本文献已被 CNKI 万方数据 SpringerLink 等数据库收录! |
|