核密度估计的随机加权逼近

Random weighting approach for kernel density estimation

目的证明核密度估计随机加权逼近的有效性。方法用随机加权法对核密度进行估计。结果在适当的条件下,(nh_n)^(1/2)(■_n(x)-fn(x))和(nh_n)^(1/2)(f_n(x)-f(x))对几乎所有的样本序列X_1,X_2…具有相同的极限分布,同时,得到了随机加权逼近的收敛速度。结论用随机加权法对核密度进行估计是可行的。

Aim To prove the validity of random weighting estimation approximation for kernel density. Methods Use the random weighting methods to estimate the kernel density. Results The results show that under certain condition,√nhn（Hn（x）-fn（x））and √nhn（fn（x）-f（x））have a same Limit Distribution for almost all series X1 ,X2…, also the speed of random weighting approximation is gained. Conclusion Form the study the conclusion has got that it is completely viable to estimate the kernel density with the random weighting methods.