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	Local generalized empirical estimation of regression
	Jiang, JC ; Kjell, D
	2004
关键词	boundary adaptive Dirac delta-function local polynomial local empirical Nadaraya-Watson estimator VARIABLE BANDWIDTH SMOOTHERS
英文摘要	Let f(x) be the density of a design variable X and m(x) = E[Y\X = x] the regression function. Then m(x) = G(x)/f (x), where G(x) = m(x)f (x). The Dirac delta-function is used to define a generalized empirical function G,(x) for G(x) whose expectation equals G(x). This generalized empirical function exists only in the space of Schwartz distributions, so we introduce a local polynomial of order p approximation to G(n)((.)) which provides estimators of the function G(x) and its derivatives. The density f (x) can be estimated in a similar manner. The resulting local generalized empirical estimator (LGE) of m(x) is exactly the Nadaraya-Watson estimator at interior points when p = 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 with p = 1 compares favorably with the Nadaraya-Watson and the popular local linear regression smoother.; Mathematics, Applied; Mathematics; SCI(E); EI; 0; ARTICLE; 1; 114-127; 47
语种	英语
出处	SCI
出版者	science in china series a mathematics
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/158008]
专题	数学科学学院
推荐引用方式 GB/T 7714	Jiang, JC,Kjell, D. Local generalized empirical estimation of regression. 2004-01-01.

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