BAHADUR'S REPRESENTATION FOR NEAREST NEIGHBOR MEDIAN ESTIMATES: THE FIXED DESIGN CASE  

作　　者：YANG Ying(Department of Probability and Statistics, Peking University, Beijing 100871, China)WANG Bingzhang(Department of Mathematics and Information Science, Yantai University, Yantai 264005, China) 

出　　处：《Systems Science and Mathematical Sciences》1999年第2期133-144,共12页

摘　　要：Consider the nonparametric regression model Yi=g(xi) +ei, i=1, 2,...,where g is an unknown function defined on the interval [0, 1], the fixed design points xi(i≥1) are known and ei’s are i.i.d. random variables with median zero. The regressor is assumed to take values in [0, 1]∈ R and the regressand to be real valued. This paper stu-dies the behavior of the nearest neighbor median estimate gnh(x)=m(Yn1(x), Yn2(x),...,Ynh(x)), where h is the number of the nearest neighbor. Under suitable conditions, Bahadur’s representation for the above-mentioned the nonparametric regression function g is obtained. Law of iterated logarithm and asymptotic normality are also established.Consider the nonparametric regression model Yi=g(xi) +ei, i=1, 2,...,where g is an unknown function defined on the interval [0, 1], the fixed design points xi(i≥1) are known and ei's are i.i.d. random variables with median zero. The regressor is assumed to take values in [0, 1]∈ R and the regressand to be real valued. This paper stu-dies the behavior of the nearest neighbor median estimate gnh(x)=m(Yn1(x), Yn2(x),...,Ynh(x)), where h is the number of the nearest neighbor. Under suitable conditions, Bahadur's representation for the above-mentioned the nonparametric regression function g is obtained. Law of iterated logarithm and asymptotic normality are also established.

关 键 词：Nearest neighbor MEDIAN ESTIMATES Bahadur’s REPRESENTATION asymptotic NORMALITY law of ITERATED logarithm. 

分 类 号：O172[理学—数学]