4,242 research outputs found
Consistency of Bayes factor for nonnested model selection when the model dimension grows
Zellner's -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 , 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 for and for 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.Comment: Published at http://dx.doi.org/10.3150/15-BEJ720 in the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Bayesian predictive densities for linear regression models under alpha-divergence loss: some results and open problems
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
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