Asymptotic Normality of the Nearest Neighbor Density Estimators under Strong Mixing Samples

DOI：

 作者 单位 秦永松 广西师范大学数学系, 广西　桂林\ 541004. 雷庆祝 广西师范大学数学系, 广西　桂林\ 541004.

研究了 $\alpha$-\!\!混合样本下最近邻密度估计的渐近性质, 证明了估计的渐近正态性并且给出了其渐近方差的显式表达式, 由此构造了 $\alpha$-\!\!混合样本下概率密度的渐近置信区间.

In this paper, the asymptotic normality of a nearest neighbor density estimator under an $\alpha$-mixing sample is studied. The authors obtain the asymptotic normality of the estimator with an explicit form of the asymptotic variance, which is used to construct the asymptotic confidence interval for a probability density function under an $\alpha$-mixing sample.