Finite Sample Bias Reduction for Misspecified Models With Extensions to High Dimensional Data

Abstract

While maximum likelihood estimates (MLEs) from generalized linear models have desirable asymptotic properties, for finite samples, these estimates can be biased for finite samples. Current bias reduction methods account for either misspecification of the model or separation in the data; however current methods cannot address both simultaneously. We provide a detailed characterization of the finite sample bias for log-linear models to understand how model components contribute to the bias of MLEs. This dissertation proposes a new robust bias reduction method that effectively reduces finite sample bias in the presence of misspecification and separation and does not result in a loss of asymptotic performance. These results are demonstrated analytically as well as empirically through simulations. This method is extended to clustered data using modified generalized estimating equations. We explore the effects finite sample bias and bias reduction methods have on transformed estimates as well as developing a post-transformation bias reduction process. The effects of finite sample bias and bias reduction methods are also explored for meta-analysis. Lastly, we discuss scenarios where these bias reduction methods may or may not be effective in high dimensional data settings with a focus on sparse models.