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

BAHADUR'S REPRESENTATION FOR NEAREST NEIGHBOR MEDIAN ESTIMATES: THE FIXED DESIGN CASE
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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.
出处 《Systems Science and Mathematical Sciences》 SCIE EI CSCD 1999年第2期133-144,共12页
关键词 Nearest neighbor MEDIAN ESTIMATES Bahadur’s REPRESENTATION asymptotic NORMALITY law of ITERATED logarithm. Nearest neighbor median estimates, Bahadur's representation, asymptotic normality, law of iterated logarithm.
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