异方差回归模型近邻型估计的相合性  

CONSISTENCY OF A NEAREST NEIGHBOR ESTIMATION IN HETEROSCEDASTICITY REGRESSION MODEL

作　　者：程业斌[1] 胡舒合[1] 

机构地区：[1]安徽大学数学系

出　　处：《高校应用数学学报（A辑）》1999年第2期169-177,共9页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金

摘　　要：本文研究异方差回归模型Ｙ（ｎ）ｉ＝ｇ（ｘ（ｎ）ｉ）＋ε（ｎ）ｉ，ｉ＝１，…，ｎ，其中ｇ是未知实函数，ｘ（ｎ）ｉ是非随机设计点列，ε（ｎ）ｉ是随机误差．文中定义了一类ｇ（ｘ）的近邻型估计ｇｎ（ｘ）＝ｎｉ＝１Ｗｎｉ（ｘ）Ｙ（ｎ）ｉ，得到了ｒ阶平均相合和渐近正态性．特别，在∞ｎ＝１ｎｉ＝１Ｅ｜ε（ｎ）ｉ｜ｓ／（ｎｉ）ｓ／ｒ＜∞，ｍａｘ１≤ｉ≤ｎＥ｜ε（ｎ）ｉ｜ｓ＝Ｏ（ｎｓ／ｒ）（某ｓ＞ｒ＞２）下，获得了ｇｎ（ｘ）的强相合和一致强相合性．In this paper, the heteroscedasticity regression model Y (n) i=g(x (n) i)+ε (n) i,i=1,…,n , is studied, where g is an unknown function, x (n) i are known and nonrandom,and ε (n) i are independent random errors. Under suitable conditions, a nearest neighbor estimate g n(x)=ni=1W ni (x)Y (n) i of g(x) is defined.It is shown that the g n is r th mean consistent and asymptotically normal.Especially,the strong consistency and uniform strong consistency for g n(x) are also obtained,provided that ∞n=1ni=1E|ε (n) i| s/(ni) s/r <∞ and max 1≤ i ≤ nE|ε (n) i| s =O(n s/r ) for some s>r >2.

关 键 词：异方差回归模型 近邻型估计 渐近正态性 相合性 

分 类 号：O212.7[理学—概率论与数理统计]