核实数据下的递归核密度估计

Recursive Kernel Estimation of Probability Density Function with Validation Data

基于替代与核实数据样本下的总体密度函数估计问题,定义一个递归型核密度的估计量,它包含替代数据和核实数据两种信息,并证明了该估计量的渐近正态性.模拟结果表明:给定样本总数N的情况下,模拟效果随核实数据样本容量n的增加而渐好;当固定核实数据样本容量n时,顶部随样本总量N的增加模拟效果渐好,尾部变差;如果同时增大N和n,模拟结果更趋近于f(x),并且也更平滑.

In consideration of the probability density estimation problem with surrogate and validation data, a recursive kernel estimation of probability density function is so defined to comprise both surrogate and validation variates that the proposed estimators are proved to be asymptotically normal. The simulation results indicate at a given constant of N, the total number of data, the method performs better as the validation variate n increases. Also, for a given n, simulation result becomes better in terms of top as N increases, but becomes bad in terms of tail. We also noted that the simulation result, as N and n together increases, more approaches the f（x） and is smoothing.