  This paper considers estimation of the predictive density for a normal linear
model with unknown variance under alpha-divergence loss for -1 <= alpha <= 1.
We first give a general canonical form for the problem, and then give general
expressions for the generalized Bayes solution under the above loss for each
alpha. For a particular class of hierarchical generalized priors studied in
Maruyama and Strawderman (2005, 2006) for the problems of estimating the mean
vector and the variance respectively, we give the generalized Bayes predictive
density. Additionally, we show that, for a subclass of these priors, the
resulting estimator dominates the generalized Bayes estimator with respect to
the right invariant prior when alpha=1, i.e., the best (fully) equivariant
minimax estimator.
