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

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.