統計学輪講（第１５回）

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.