负相关随机变量密度小波估计的L^(p)-相合性

L^(p)-consistency of wavelet density estimation for negatively dependent random variables

目的 基于负相关随机样本,对密度函数进行估计。方法 利用负相依样本的性质、Jensen不等式和Lebesgue控制收敛定理给出证明过程。结果与结论小波估计器能够对负相关样本的密度函数进行有效估计,为进一步计算小波估计器的收敛阶和讨论最优性提供理论依据。

Purposes—To estimate the density function of negatively dependent random samples.Methods—The process of proof is shown by using properties of negatively dependent samples,Jensen's inequality and Lebesgue's dominated convergence theorem.Results and Conclusions—The wavelet can estimate the density function of negatively dependent samples well,which provides theoretical basis for calculating convergence rates and studying the optimality of wavelet estimators.