数学物理学报(英文版) ›› 1995, Vol. 15 ›› Issue (S1): 1-10.
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高集体
Gao Jiti
摘要: Consider the regression model y1=x1β+g(t1)+ei for i=1,2,…, n. Here the design points (xi,ti) are known and nonrandom, and ei are random errors. The family of nonparametric estimates of ĝn(·) of g(·) including known estimates proposed by Gasser & Muller[1] is also proposed to be a class of new nearest neighbor estimates of g(·). Based on the nonparametric regression procedures, we investigate a statistic for testing H0:g=0, and obtain some asymptotic results about estimates.