Analysis of multi-unit variance components models with state space profiles

作     者：Tsimikas, JV Ledolter, J 

作者机构：Harvard Univ Sch Med Dept Hlth Care Policy Boston MA 02115 USA Univ Iowa Dept Stat & Actuarial Sci Iowa City IA 52242 USA 

出 版 物：《ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS》 (统计数理研究所纪事)

年 卷 期：1998年第50卷第1期

页      面：147-164页

核心收录：

学科分类：07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：continuous-time stochastic models EM algorithm Kalman Filter mixed model prediction restricted maximum likelihood smoothing splines unequally spaced observations variance components 

摘      要：We apply the Kalman Filter to the analysis of multi-unit variance components models where each unit s response profile follows a state space model. We use mixed model results to obtain estimates of unit-specific random effects, state disturbance terms and residual noise terms. We use the signal extraction approach to smooth individual profiles. We show how to utilize the Kalman Filter to efficiently compute the restricted loglikelihood of the model. For the important special case where each unit s response profile follows a continuous structural time series model with known transition matrix we derive an EM algorithm for the restricted maximum likelihood (REML) estimation of the variance components. We present details for the case where individual profiles are modeled as local polynomial trends or polynomial smoothing splines.