Weight choice by minimizing MSE for general likelihood averaging

no issnIn model averaging a weighted estimator is constructed based on a set of models, extending model selection where a single estimator is constructed from one selected model found via an information criterion. Several studies discuss the weight choice for linear models only and almost all studies assign weights to models by using optimization routines, specifically quadratic programming and nonlinear optimization. None of these studies worried about the unicity of the estimated weights, while in fact, with those methods the chosen weight is often non-unique, resulting in difficulties with interpretations of weighted averages. Our contribution is threefold: (1) We minimize an estimator for the mean squared error in a local misspecification framework from which unique weights can be assigned to a set of 'linearly independent design matrix' models. (2) The weight choice applies to a broad range of models including generalized linear models. (3) In linear models the computational complexity of averaging may be reduced since weighted predictions from nested and singleton models are equal. In a simulation study in Poisson regression the performance of our method of averaging is compared with other such methods. The simulation results show that the proposed method performs well.status: publishe