偏正态混合效应模型中方差分量函数的参数Bootstrap推断  

Parametric Bootstrap Inference on Variance Component Functions in the Skew-normal Mixed Effects Model

作　　者：叶仁道[1] 安娜 YE Rendao;AN Na(School of Economics,Hangzhou Dianzi University,Hangzhou 310018,China)

机构地区：[1]杭州电子科技大学经济学院,浙江杭州310018

出　　处：《应用数学》2023年第2期353-363,共11页Mathematica Applicata

基　　金：国家社会科学基金(21BTJ068)。

摘　　要：偏正态混合效应模型通过引入偏度参数,以便更好地刻画实际数据偏态特征,所以被广泛应用于众多实际领域.进一步,方差分量的假设检验一直是该模型的热点研究问题.因此,有必要在偏正态分布下系统讨论混合效应模型中方差分量函数的统计推断问题.首先,分别基于参数Bootstrap方法和广义方法探讨单个方差分量、方差分量之和、方差分量之比的单边假设检验和区间估计问题.其次,Monte Carlo结果表明,在所给样本量和参数设置下,参数Bootstrap方法大多数情况下优于广义方法.最后,将上述方法应用于空气质量指数的案例研究中,以验证所给方法的合理性与有效性.The skew-normal mixed effects model introduces skewness parameter to better describe the skewness characteristic of actual data.Therefore,it is widely used in many practical fields.Furthermore,the hypothesis testing of variance components has always been a hot research issue of this model.Therefore,it is necessary to systematically discuss the statistical inference of the variance component functions in the mixed effects model under the skew-normal distribution.Firstly,using the parametric Bootstrap approach and generalized approach,the one-sided hypothesis testing and interval estimation problems for the single variance component,the sum and ratio of variance components are discussed respectively.Further,the Monte Carlo simulation results indicate that the parametric Bootstrap approach is better than the generalized approach in most cases under the given sample size and parameter setting.Finally,the above approaches are applied to the real data example of the air quality index to verify their rationality and effectiveness.

关 键 词：偏正态混合效应模型 方差分量函数 BOOTSTRAP 广义方法 

分 类 号：O212.1[理学—概率论与数理统计]