函数型非参数密度伪估计的一致收敛速度  

Rate of Consistency Convergence for Nonparametric Pseudo-estimates with Functional Variables

作　　者：陈文勇[1] 凌能祥[1] 

机构地区：[1]合肥工业大学数学学院,安徽合肥232001

出　　处：《安庆师范学院学报（自然科学版）》2011年第2期25-28,38,共5页Journal of Anqing Teachers College(Natural Science Edition)

摘　　要：首先构造函数型非参数随机变量X的密度伪估计~f（x）和众数θ的估计nθ,在比较自然的条件下,得到基于独立同分布函数型数据非参数密度伪估计的几乎完全一致收敛速度,以及基于函数型独立场合下非参数众数估计θn的几乎完全一致收敛速度,并推广了现有文献的相关结论。Our main aim is to design a density pseudo-estimators（x） and mode estimators θn of nonparametric functional variables X.It is shown that the rate of consistency of the mode estimator for the density pseudo-estimator can be determined with some natural conditions.Indeed,our approach is to prove the rate of uniform convergence of the density pseudo-estimators of some nonparametric models in i.i.d.case and we establish the almost complete convergence rate of the mode estimators θn which extend the existing literature related results in i.i.d.case.

关 键 词：密度伪估计 众数 小球概率 一致收敛 

分 类 号：O212.7[理学—概率论与数理统计]