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	Asymptotic theory of nonparametric regression estimates with censored data
	Shi, PD ; Wang, HY ; Zhang, LH
	2000
关键词	nonparametric regression censored data regression spline optimal rates of convergence PRODUCT-LIMIT ESTIMATOR LINEAR-MODEL
英文摘要	For regression analysis, some useful information may have been lost when the responses are right censored. To estimate nonparametric functions, several estimates based on censored data have been proposed and their consistency and convergence rates have been studied in literature, but the optimal rates of global convergence have not been obtained yet. Because of the possible information loss, one may think that it is impossible for an estimate based on censored data to achieve the optimal rates of global convergence for nonparametric regression, which were established by Stone based on complete data. This paper constructs a regression spline estimate of a general nonparametric regression function based on right-censored response data, and proves, under some regularity conditions, that this estimate achieves the optimal rates of global convergence for nonparametric regression. Since the parameters for the nonparametric regression estimate have to be chosen based on a data driven criterion, we also obtain the asymptotic optimality of AIC, AICC, GCV, C-p and FPE criteria in the process of selecting the parameters.; Mathematics, Applied; Mathematics; SCI(E); EI; 0; ARTICLE; 6; 574-580; 43
语种	英语
出处	SCI ; EI
出版者	science in china series a mathematics physics astronomy
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/213473]
专题	数学科学学院
推荐引用方式 GB/T 7714	Shi, PD,Wang, HY,Zhang, LH. Asymptotic theory of nonparametric regression estimates with censored data. 2000-01-01.

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