相依样本条件t-分位数核估计的强收敛速度  

Strong Consistency Rates of Conditional t-Quantiles Kernel Estimator for Mixing Sample

作　　者：安军[1] 袁德美[1] 

机构地区：[1]重庆工商大学理学院,重庆400067

出　　处：《西南师范大学学报（自然科学版）》2004年第3期354-356,共3页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：重庆市教委科研基金资助项目(010702);重庆工商大学科研基金资助项目.

摘　　要：在一定条件下,得到了φ混合样本条件t分位数的核估计强收敛速度,即定理　对同分布的φ混合样本(X1,Y1),…,(Xn,Yn)∈Rd×R1,若 X1具有边际密度函数f; 条件分布函数F(y｜x)在(x,θx(t))的邻域内具有连续的密度函数f(y｜x); ∑nφ(n)<∞; h=(n-12logn)1d+1,0<Mn→∞.则θx(t)(0<t<1)的核估计θx,n(t)的强相合速度可以达到on-12logn1d+1Mn.For conditional t-quantiles kernel estimator of mixing sample, in this paper, we obtain its consistency rates under certain conditions. That is, for identically distributed φ-mixing samples, (X_1, Y_1), …, (X_n, Y_n)∈R^d×R^1, if? X_1 has marginal density function f;? conditional distribution function F(y｜x) has continuous density function f(y｜x) in the neighborhood of (x, θ_x(t));? ∑nφ(n)<∞;? h=n~~^(-12)logn~~^(1d+1), 0<M_n→∞.then the strong consistency rates of kernel estimate θ_(x,n)(t) for θ_x(t)(0<t<1) attains on~~^(-12)logn~~^(1d+1)M_n.

关 键 词：条件t-分位数 Ψ-混合 核估计 收敛速度 

分 类 号：O212.7[理学—概率论与数理统计]