多个偏正态总体共同位置参数的Bootstrap置信区间  

Bootstrap Confidence Intervals for the Common Location Parameter of Several Skew-Normal Populations

作　　者：叶仁道[1] 王仲池 罗堃[2] 林雅 Ye Rendao;Wang Zhongchi;Luo Kun;Lin Ya(School of Economics,Hangzhou Dianzi University,Hangzhou 310018;Alibaba Business College,Hangzhou Normal University,Hangzhou 310036)

机构地区：[1]杭州电子科技大学经济学院,杭州310018 [2]杭州师范大学阿里巴巴商学院,杭州310036

出　　处：《数学物理学报（A辑）》2021年第1期194-216,共23页Acta Mathematica Scientia

基　　金：教育部人文社会科学研究项目(19YJA910006);浙江省自然科学基金(LY20A010019);浙江省属高校基本科研业务费专项资金(GK199900299012-204);国家自然科学基金(11401148)。

摘　　要：该文基于Bootstrap方法研究多个偏正态总体共同位置参数的区间估计和假设检验问题.首先,分别给出未知参数的矩估计和极大似然估计.其次,将徐礼文[1]对多个正态总体共同均值的探讨推广到多个偏正态总体,进而构造共同位置参数的Bootstrap置信区间和Bootstrap检验统计量.Monte Carlo模拟结果表明,无论是两个总体、三个总体还是五个总体,基于矩估计和惩罚极大似然估计的Bootstrap置信区间在覆盖概率意义下优于其他四种Bootstrap置信区间.最后,将上述方法应用于地区生产总值和生物利用度数据的案例分析,以验证该文所给方法的合理性和有效性.In this paper,we consider the interval estimation and hypothesis testing problems for the common location parameter of several skew-normal populations when the scale parameters and skewness parameters are unknown.Firstly,we estimate the unknown parameters using the methods of moment estimation and maximum likelihood estimation.Secondly,the Bootstrap confidence intervals and Bootstrap test statistics are constructed,which generalize the results given by Xu[1]under several normal populations.Thirdly,the Monte Carlo simulation results indicate that the Bootstrap confidence intervals based on the methods of moment estimation and maximum penalized likelihood estimation perform better than other four confidence intervals.Finally,the above approaches are applied to the real data examples of regional gross domestic product of China and bioavailability in order to verify the reasonableness and effectiveness of the proposed approaches.

关 键 词：偏正态总体 共同位置参数 矩估计 极大似然估计 Bootstrap置信区间 

分 类 号：O212[理学—概率论与数理统计]