We propose a new classified mixed model prediction (CMMP) procedure, called pseudo-Bayesian CMMP, that utilizes network information in matching the group index between the training data and new data, whose characteristics of interest one wishes to predict. The original CMMP procedure (Jiang et al. 2018) does not incorporate such information; as a result, the method is not consistent in terms of matching the group index. Although, as the number of training data groups increases, the original CMMP method can predict the mixed effects of interest consistently, its accuracy is not guaranteed when the number of groups is moderate, as is the case in many potential applications. The proposed pseudo-Bayesian CMMP procedure assumes a flexible working probability model for the group index of the new observation to match the index of a training data group, which may be viewed as a pseudo prior. We show that, given any working model satisfying mild conditions, the pseudo-Bayesian CMMP procedure is consistent and asymptotically optimal both in term of matching the group index and in terms of predicting the mixed effect of interest associated with the new observations. The theoretical results are fully supported by results of empirical studies, including Monte-Carlo simulations and real-data validation. This work is joint with Haiqiang Ma of Jiangxi University of Finance and Economics.
About the Speaker:
蒋继明，加利福尼亚大学|以诚为本·赢在信誉9001戴维斯分校统计系教授，主要研究领域为混合效应模型、模型选择、小区域估计、纵向数据分析、精准医学、大数据智能、统计遗传学/生物信息学、药代动力学和渐近理论。发表论文100余篇，大多数发表在The Annals of Statistics、 Journal of the American Statistical Association, Journal of the Royal Statistical Society, Series B 和 Biometrika等顶级统计和生物统计学期刊上，著有七本专著，包括Linear and Generalized Linear Mixed Models and Their Applications (Springer 2007; 2nd ed. 2021), Large Sample Techniques for Statistics (Springer 2010; 2nd ed. 2022), The Fence Methods (World Scientific 2015; joint with Nguyen), Asymptotic Analysis of Mixed Effects Models: Theory, Application, and Open Problems (Chapman & Hall/CRC, 2017), Robust Mixed Model Analysis (World Scientific 2019). 多次受邀参加相关领域的国际学术会议并作大会主旨报告，先后被选为Institute of Mathematical Statistics (IMS；数理统计学会)，American Association for the Advancement of Science (AAAS; 美国科学促进协会)，American Statistical Association (ASA；美国统计学会)，International Statistical Institute (ISI；国际统计研究院)等国际著名统计协会的Fellow，长期担任Journal of American Statistical Association、The Annals of Statistics等学术期刊的副主编，曾获得美国统计协会的杰出统计应用奖以及美国国家科学基金会和美国国立卫生研究院颁发的众多奖项。
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