高维非均匀核N.N.估计的强一致收敛速度  

STRONG UNIFORM CONVERGENCE RATES OF MULTI-DIMENSIONAL N.N.DENSITY ESTIMATES WITH NON-UNIFORM KERNEL

作　　者：张涤新[1] 

机构地区：[1]贵州财经学院科研处

出　　处：《高校应用数学学报（A辑）》1996年第1期41-52,共12页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金;贵州自然科学基金

摘　　要：本文讨论了高维空间中非均匀核N.N.估计的一致强收敛速度。在密度函数的条件与[1,2]相同时,得到了比[1,2]更好伪收敛速度,就其收敛的主要部分而言已无可改进。由于均匀核N.N.估计是非均匀核N.N.估计的特例,从而大大拓广了N.N.估计的理论价值和应用范围。In this paper, we study the strong uniform convergence rates of multi-dimensional N.N. estimates with non-uniform kernel. When the conditions of density function are thesame as those in [1] and [2], we obtain convergence rates better than those in [1] and[2], but the rates are not improved for the main part of convergence. Since the N. N. esti-mate with uniform kernel is the special example of N. N. estimates with non-uniform ker-nel, the results are very useful in theory and applications.

关 键 词：非均匀核 收敛速度 强一致收敛速度 最近邻估计 

分 类 号：O212.7[理学—概率论与数理统计]