相依样本下密度函数及其导函数的相合随机窗宽核估计  

Kernal Estimates of Random Window Width of Density Function and its Derivatives Under Dependent Asmple

作　　者：薛留根 

机构地区：[1]河南许昌师范专科学校,许昌461000

出　　处：《数理统计与应用概率》1994年第3期54-60,共7页

摘　　要：设{X_n}是R^1中的平稳、强混合序列,具有公共的密度f(x),则可定义f(x)及其导函数f^(r)(x)的核估计与最近邻估计 f_n^(r)(x)=(nh_n^(r+1)(x))^(-1) sum from i=1 to n K^(r)((X_i-x)/h_n(x)) f_n(x)=(na_n(x))^(-1)sum from i=1 to n K((X_i-x)/a_n(x))其中核函数K(x)为取定的概率密度函数,且具有r(r≥0)阶导数,窗宽h_n(x)=h_n(x;X_1,…,X_n)>0与x,X1,…,X_n有关,a_n(x)为x到X_1,…,X_n中第k_n个最近点的距离。本文在样本序列为平稳强混合的情况下,研究凶f_n^(r)(x)的强一致相合性,并将所得结果应用于最近邻估计,得到了较好的结论。Let X1,…, Xn be a random asmple taking values in R 1 with a comon probabitily density f(x), then the kernel estimates and the nearest neighbor estimate of f(r)(x) and f(x) are definedwhere K(x) is a probability density with rth order derivative, and hn(x) = hn(x; X1,…, Xn) > 0 depend on x, X1,…, Xn, and an(x) is the distance of x between kn th nearest point in X1,…, Xn. In this paper, we study the strong uniform consistency of fn(r) (x) and fn(x), and obtain very good results.

关 键 词：相依样本 密度函数 核估计 

分 类 号：O211.67[理学—概率论与数理统计]