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We consider the problem of variable selection in linear regression using
mixtures of g-priors. A number of mixtures have been 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, more specifically when p = O(n b ), 0 < b < 1. The marginal density based
on the proposed mixture has a nice approximation with a closed form expression,
which makes application of the method as tractable as an information criterion-based
method. The proposed method satisfies fundamental properties like model selection
consistency when the true model lies in the model space, and also consistency in an
appropriate sense, under misspecified models setup. The method is quite robust in the
sense that the above properties are not confined to normal linear models; they continue
to hold under reasonable conditions for a general class of error distributions. Finally,
we compare the performance of the proposed prior theoretically with that of some
other mixtures of g-priors. We also compare it with several other Bayesian methods of
model selection using simulated data sets. Theoretically, as well as in simulations, it
emerges that unlike most of the other methods of model selection, the proposed prior
is competent enough while selecting the true model irrespective of its dimension.