Technical Report Series COMPARISON OF FOUR SMALL SAMPLE BIAS CORRECTIONS OF THE EMPIRICAL COVARIANCE ESTIMATORS

The empirical (sandwich or robust) covariance matrix, usually used in conjunction with Generalized Estimating Equations (GEE) and Generalized Linear Mixed Models (GLMM), is biased towards zero for small sample sizes. As a consequence of this bias Type I error rates are usually higher than the nominal levels. Several small sample bias corrections have been proposed in the literature. The purpose of this technical report is to study the performance of four commonly used small sample bias corrections via simulation studies. Three of these four are already available as options in the SAS procedure GLIMMIX. The fourth one was proposed by Morel, Bokossa and Neerchal (2003). We show that all these corrections can be obtained as special cases of a general form. We discuss their rank properties and show that our proposed correction always provides full rank covariance estimators whenever the model based covariance estimator is positive definite. An example is provided to highlight this property.