Robust small-sample inference for fixed effects in general Gaussian linear models

Although asymptotically, the empirical covariance estimator is consistent and robust with respect to the selection of the working correlation matrix, when the sample size is small, its bias may not be negligible. This article proposes a small sample correction for the empirical covariance estimator in general Gaussian linear models. Inference for the fixed effects based on the corrected covariance matrix is also derived. A two-way analysis of variance (ANOVA) model with repeated measures, which evaluates the effectiveness of a CB1 receptor antagonist, and a four-period crossover design, which assesses the treatment effect in subjects with intermittent claudication, serve as examples to illustrate the proposed and other investigated methods. Simulation studies show that the proposed method generally performs better than other bias-correction methods, including Mancl and DeRouen (2001), Kauermann and Carroll (2001), and Fay and Graubard (2001), in the investigated balanced designs.