负相依样本的Rosenthal型不等式  

On Rosenthal's inequality for negatively-dependent samples

作　　者：陈磊 许俊莲 CHEN Lei;XU Jun-lian(Institute of Physics and Optoelectronics Technology, Baoji University of Arts and Sciences, Baoji 721016, Shaanxi, China;School of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji 721013, Shaanxi, China)

机构地区：[1]宝鸡文理学院物理与光电技术学院,陕西宝鸡721016 [2]宝鸡文理学院数学与信息科学学院,陕西宝鸡721013

出　　处：《宝鸡文理学院学报（自然科学版）》2021年第3期5-7,共3页Journal of Baoji University of Arts and Sciences(Natural Science Edition)

基　　金：陕西省自然科学基金项目(2020JQ-892)。

摘　　要：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.

关 键 词：Rosenthal不等式 负相依 Markov不等式 JENSEN不等式 单调函数 

分 类 号：O174.2[理学—数学]