93 research outputs found
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
On the behavior of Bayesian credible intervals for some restricted parameter space problems
For estimating a positive normal mean, Zhang and Woodroofe (2003) as well as
Roe and Woodroofe (2000) investigate 100( HPD credible sets
associated with priors obtained as the truncation of noninformative priors onto
the restricted parameter space. Namely, they establish the attractive lower
bound of for the frequentist coverage probability
of these procedures. In this work, we establish that the lower bound of
is applicable for a substantially more general
setting with underlying distributional symmetry, and obtain various other
properties. The derivations are unified and are driven by the choice of a right
Haar invariant prior. Investigations of non-symmetric models are carried out
and similar results are obtained. Namely, (i) we show that the lower bound
still applies for certain types of asymmetry (or
skewness), and (ii) we extend results obtained by Zhang and Woodroofe (2002)
for estimating the scale parameter of a Fisher distribution; which arises in
estimating the ratio of variance components in a one-way balanced random
effects ANOVA. Finally, various examples illustrating the wide scope of
applications are expanded upon. Examples include estimating parameters in
location models and location-scale models, estimating scale parameters in scale
models, estimating linear combinations of location parameters such as
differences, estimating ratios of scale parameters, and problems with
non-independent observations.Comment: Published at http://dx.doi.org/10.1214/074921706000000635 in the IMS
Lecture Notes--Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
A unified minimax result for restricted parameter spaces
We provide a development that unifies, simplifies and extends considerably a
number of minimax results in the restricted parameter space literature. Various
applications follow, such as that of estimating location or scale parameters
under a lower (or upper) bound restriction, location parameter vectors
restricted to a polyhedral cone, scale parameters subject to restricted ratios
or products, linear combinations of restricted location parameters, location
parameters bounded to an interval with unknown scale, quantiles for
location-scale families with parametric restrictions and restricted covariance
matrices.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ336 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
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