344 research outputs found
Rejoinder: Conditional Growth Charts
Rejoinder: Conditional Growth Charts [math.ST/0702634]Comment: Published at http://dx.doi.org/10.1214/009053606000000678 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Discussion paper. Conditional growth charts
Growth charts are often more informative when they are customized per
subject, taking into account prior measurements and possibly other covariates
of the subject. We study a global semiparametric quantile regression model that
has the ability to estimate conditional quantiles without the usual
distributional assumptions. The model can be estimated from longitudinal
reference data with irregular measurement times and with some level of
robustness against outliers, and it is also flexible for including covariate
information. We propose a rank score test for large sample inference on
covariates, and develop a new model assessment tool for longitudinal growth
data. Our research indicates that the global model has the potential to be a
very useful tool in conditional growth chart analysis.Comment: This paper discussed in: [math/0702636], [math/0702640],
[math/0702641], [math/0702642]. Rejoinder in [math.ST/0702643]. Published at
http://dx.doi.org/10.1214/009053606000000623 in the Annals of Statistics
(http://www.imstat.org/aos/) by the Institute of Mathematical Statistics
(http://www.imstat.org
Bayesian variable selection with shrinking and diffusing priors
We consider a Bayesian approach to variable selection in the presence of high
dimensional covariates based on a hierarchical model that places prior
distributions on the regression coefficients as well as on the model space. We
adopt the well-known spike and slab Gaussian priors with a distinct feature,
that is, the prior variances depend on the sample size through which
appropriate shrinkage can be achieved. We show the strong selection consistency
of the proposed method in the sense that the posterior probability of the true
model converges to one even when the number of covariates grows nearly
exponentially with the sample size. This is arguably the strongest selection
consistency result that has been available in the Bayesian variable selection
literature; yet the proposed method can be carried out through posterior
sampling with a simple Gibbs sampler. Furthermore, we argue that the proposed
method is asymptotically similar to model selection with the penalty. We
also demonstrate through empirical work the fine performance of the proposed
approach relative to some state of the art alternatives.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1207 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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