  Zellner's $g$-prior is a popular prior choice for the model selection
problems in the context of normal regression models. Wang and Sun [J. Statist.
Plann. Inference 147 (2014) 95-105] recently adopt this prior and put a special
hyper-prior for $g$, which results in a closed-form expression of Bayes factor
for nested linear model comparisons. They have shown that under very general
conditions, the Bayes factor is consistent when two competing models are of
order $O(n^{\tau})$ for $\tau <1$ and for $\tau=1$ is almost consistent except
a small inconsistency region around the null hypothesis. In this paper, we
study Bayes factor consistency for nonnested linear models with a growing
number of parameters. Some of the proposed results generalize the ones of the
Bayes factor for the case of nested linear models. Specifically, we compare the
asymptotic behaviors between the proposed Bayes factor and the intrinsic Bayes
factor in the literature.
