中文摘要：

目的研究核密度的随机加权估计,在一定条件下证明核密度的随机加权估计是有效的。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√nhn（Hn（x）-fn（x））和√nhn（fn（x）-f（x））对几乎所有的样本序列X1,X2,…具有相同的极限分布,即随机加权逼近成立。结论所提出的随机加权估计优于钱伟民所做的Bootstrap估计,提高了估计的精度。

英文摘要：

Aim To study random weighting estimation for kernel density,and on certain condition to prove the validity of random weighting estimation for kernel density.Methods The kernel density is estimated by the random weighting methods.Results The results show that under proper condition,nhn√nhn（fn（x）-f（x）） and √nhn（fn（x）-f（x）） have a same limit distribution for almost all series X1,X2…,namely,random weighting approximation comes into existence.Conclusion The results of research show that the random weighting method is better than Bootstrap estimation in literature [2].The accuracy of estimation is improved.