Robust inference in linear mixed model with skew normal-symmetric error  

作　　者：Mixia WU Ye TIAN Aiyi LIU 

机构地区：[1]College of Applied Sciences, Beijing University of Technology, Beijing 100124, China [2]Biostatistics and Bioinformatics Branch, Eunice Kennedy Shriver National Institute of Child Health and Human Development, Bethesda, MD 20892, USA

出　　处：《Frontiers of Mathematics in China》2017年第6期1483-1500,共18页中国高等学校学术文摘·数学（英文）

基　　金：The authors are grateful to the referees for their valuable suggestions which considerably improved the paper. This work was supported by the National Natural Science Foundation of China （Grant Nos. 11171011, 11471036）, the Natural Science Foundation of Beijing （Grant No. 1132007）, and Beijing Municipal Science and Technology Project （Grant No. km201410005011）. Research of A. Liu was supported by the Intramural Research Program of the Eunice Kennedy Shriver National Institute of Child Health and Human Development （NICHD） and the National Institutes of Health （NIH）.

摘　　要：Linear mixed effects models with general skew normal-symmetric （SNS） error are considered and several properties of the SNS distributions are obtained. Under the SNS settings, ANOVA-type estimates of variance components in the model are unbiased, the ANOVA-type F-tests are exact F-tests in SNS setting, and the exact confidence intervals for fixed effects are constructed. Also the power of ANOVA-type F-tests for components are free of the skewing function if the random effects normally distributed. For illustration of the main results, simulation studies on the robustness of the models are given by comparisons of multivariate skew-normal, multivariate skew normal-Laplace, multivariate skew normal-uniform, multivariate skew normal-symmetric, and multivariate normal distributed errors. A real example is provided for the illustration of the proposed method.Linear mixed effects models with general skew normal-symmetric （SNS） error are considered and several properties of the SNS distributions are obtained. Under the SNS settings, ANOVA-type estimates of variance components in the model are unbiased, the ANOVA-type F-tests are exact F-tests in SNS setting, and the exact confidence intervals for fixed effects are constructed. Also the power of ANOVA-type F-tests for components are free of the skewing function if the random effects normally distributed. For illustration of the main results, simulation studies on the robustness of the models are given by comparisons of multivariate skew-normal, multivariate skew normal-Laplace, multivariate skew normal-uniform, multivariate skew normal-symmetric, and multivariate normal distributed errors. A real example is provided for the illustration of the proposed method.

关 键 词：Skew normal-symmetric （SNS） ANOVA-type F-test mixed effect 

分 类 号：T0[一般工业技术]