統計学輪講（第15回） 日時 2012年10月09日(火) 14時50分～15時40分 場所 経済学部新棟３階第３教室 講演者 小島 将裕 (経済M1) 演題 Hypothesis testing in the linear mixed model 概要 In this talk, we consider the Wald, Score and Likelihood Ratio test statistics for a linear hypothesis on regression coefficients in a linear mixed model. In the linear mixed model, the covariance matrix of observations is a function of nuisance parameter like variance components. When the parameters are estimated by ML estimators, Rothenberg(1984) derived the Bartlett corrections for the three test statistics. However, the Bartlett corrections based on the Taylor series expansion are harder to calculate for covariance matrices with more complicated structure. Another problem is that his results can not be used for REML, MINQUE and others but for ML. In this study, we not only extend his result to the general consistent estimators for the nuisance parameter, but also suggest the estimates of the Bartlett corrections based on the parameter the parametric bootstrap method.