14,309 research outputs found
ANCOVA: A global test based on a robust measure of location or quantiles when there is curvature
For two independent groups, let be some conditional measure of
location for the th group associated with some random variable , given
that some covariate . When is a robust measure of location, or
even some conditional quantile of , given , methods have been proposed
and studied that are aimed at testing : that deal with
curvature in a flexible manner. In addition, methods have been studied where
the goal is to control the probability of one or more Type I errors when
testing for each . This paper suggests a
method for testing the global hypothesis : for when using a robust or quantile location estimator.
An obvious advantage of testing hypotheses, rather than the global
hypothesis, is that it can provide information about where regression lines
differ and by how much. But the paper summarizes three general reasons to
suspect that testing the global hypothesis can have more power. 2 Data from the
Well Elderly 2 study illustrate that testing the global hypothesis can make a
practical difference.Comment: 23 pp 2 Figure
Good, great, or lucky? Screening for firms with sustained superior performance using heavy-tailed priors
This paper examines historical patterns of ROA (return on assets) for a
cohort of 53,038 publicly traded firms across 93 countries, measured over the
past 45 years. Our goal is to screen for firms whose ROA trajectories suggest
that they have systematically outperformed their peer groups over time. Such a
project faces at least three statistical difficulties: adjustment for relevant
covariates, massive multiplicity, and longitudinal dependence. We conclude
that, once these difficulties are taken into account, demonstrably superior
performance appears to be quite rare. We compare our findings with other recent
management studies on the same subject, and with the popular literature on
corporate success. Our methodological contribution is to propose a new class of
priors for use in large-scale simultaneous testing. These priors are based on
the hypergeometric inverted-beta family, and have two main attractive features:
heavy tails and computational tractability. The family is a four-parameter
generalization of the normal/inverted-beta prior, and is the natural conjugate
prior for shrinkage coefficients in a hierarchical normal model. Our results
emphasize the usefulness of these heavy-tailed priors in large multiple-testing
problems, as they have a mild rate of tail decay in the marginal likelihood
---a property long recognized to be important in testing.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS512 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
- β¦