Small sample properties of the power function ofF tests in two-way error component regression

In this paper we investigate properties of the power function of the generalized least squaresF test for linear hypotheses under regression models with two-way error component model. The covariance structure of the model depends on the correlation coefficients ρ1 and ρ2 corresponding to the random effects. This model has been frequently applied to the analysis of panel data. In general, we show that the power is a monotonically increasing function of ρ1(ρ2) in a region which is close to the ρ1(ρ2) axis, and a monotonically decreasing function of ρ1(ρ2) in a region close to the ρ2(ρ1) axis. This research is supported by the National Natural Science Foundation of China, the Natural Science Foundation of Beijing, a project of Science and Technology of Beijing Education Committee, the Academy of Finland, and the University of Tampere.