The choice of weights in frequentist model average estimators is an important but difficult problem. Liang et al. (2011) suggested a criterion for the choice of weight under a general parametric framework which is termed as the generalized OPT (GOPT) criterion in the present paper. However, no properties and applications of the criterion have been studied. This paper is devoted to the further investigation of the GOPT criterion. We show that how to use this criterion for comparison of some existing weights such as the smoothed AIC-based and BIC-based weights and for the choice between model averaging and model selection. Its connection to the Mallows and ordinary OPT criteria is built. The asymptotic optimality on the criterion in the case of non-random weights is also obtained. Finite sample performance of the GOPT criterion is assessed by simulations. Application to the analysis of two real data sets is presented as well.
This paper considers the post-J test inference in non-nested linear regression models. Post-J test inference means that the inference problem is considered by taking the first stage J test into account. We first propose a post-J test estimator and derive its asymptotic distribution. We then consider the test problem of the unknown parameters, and a Wald statistic based on the post-J test estimator is proposed. A simulation study shows that the proposed Wald statistic works perfectly as well as the two-stage test from the view of the empirical size and power in large-sample cases, and when the sample size is small, it is even better. As a result,the new Wald statistic can be used directly to test the hypotheses on the unknown parameters in non-nested linear regression models.
