  There is a rich literature proposing methods and establishing asymptotic
properties of Bayesian variable selection methods for parametric models, with a
particular focus on the normal linear regression model and an increasing
emphasis on settings in which the number of candidate predictors ($p$) diverges
with sample size ($n$). Our focus is on generalizing methods and asymptotic
theory established for mixtures of $g$-priors to semiparametric linear
regression models having unknown residual densities. Using a Dirichlet process
location mixture for the residual density, we propose a semiparametric
$g$-prior which incorporates an unknown matrix of cluster allocation
indicators. For this class of priors, posterior computation can proceed via a
straightforward stochastic search variable selection algorithm. In addition,
Bayes factor and variable selection consistency is shown to result under
various cases including proper and improper priors on $g$ and $p>n$, with the
models under comparison restricted to have model dimensions diverging at a rate
less than $n$.
