  We consider variable selection problem in linear regression using mixture of
$g$-priors. A number of mixtures are proposed in the literature which work
well, especially when the number of regressors $p$ is fixed. In this paper, we
propose a mixture of $g$-priors suitable for the case when $p$ grows with the
sample size $n$. We study the performance of the method based on the proposed
prior when $p=O(n^b),~0<b<1$. Along with model selection consistency, we also
investigate the performance of the proposed prior when the true model does not
belong to the model space considered. We find conditions under which the
proposed prior is consistent in appropriate sense when normal linear models are
considered. Further, we consider the case with non-normal errors in the
regression model and study the performance of the model selection procedure. We
also compare the performance of the proposed prior with that of several other
mixtures available in the literature, both theoretically and using simulated
data sets.
