负相依样本的Rosenthal型不等式

On Rosenthal's inequality for negatively-dependent samples

目的基于一类负相依随机样本,建立其Rosenthal型不等式。方法利用负相依样本的性质、Markov不等式和Jensen不等式给出证明过程。结果与结论成功将Rosenthal型不等式从独立样本推广到负相依样本,该不等式将为小波密度估计提供理论基础。

Purposes—To establish the Rosenthal's inequality for negatively-dependent samples.Methods—The process of proof is shown by using properties of negatively-dependent samples and Markov's and Jensen's inequalities.Result and Conclusion—The Rosenthal's inequality is successfully generalized from independent samples to negatively-dependent samples,which will provide theoretical basis for wavelet density estimation.