Confidence Statements for Ordering Quantiles

This work proposes Quor, a simple yet effective nonparametric method to compare independent samples with respect to corresponding quantiles of their populations. The method is solely based on the order statistics of the samples, and independence is its only requirement. All computations are performed using exact distributions with no need for any asymptotic considerations, and yet can be run using a fast quadratic-time dynamic programming idea. Computational performance is essential in high-dimensional domains, such as gene expression data. We describe the approach and discuss on the most important assumptions, building a parallel with assumptions and properties of widely used techniques for the same problem. Experiments using real data from biomedical studies are performed to empirically compare Quor and other methods in a classification task over a selection of high-dimensional data sets

MULTIPLE COMPARISONS WITH THE BEST: BAYESIAN PRECISION MEASURES OF EFFICIENCY RANKINGS

A large literature exists on measuring the allocative and technical efficiency of a set of firms. A segment of this literature uses data envelopment analysis (DEA), creating relative efficiency rankings that are nonstochastic and thus cannot be evaluated according to the precision of the rankings. A parallel literature uses econometric techniques to estimate stochastic production frontiers or distance functions, providing at least the possibility of computing the precision of the resulting efficiency rankings. Recently, Horrace and Schmidt (2000) have applied sampling theoretic statistical techniques known as multiple comparisons with control (MCC) and multiple comparisons with the best (MCB) to the issue of measuring the precision of efficiency rankings. This paper offers a Bayesian multiple comparison alternative that we argue is simpler to implement, gives the researcher increased exibility over the type of comparison made, and provides greater, and more in-tuitive, information content. We demonstrate this method on technical efficiency rankings of a set of U.S. electric generating firms derived within a distance function framework.Research Methods/ Statistical Methods,

Bayesian co-estimation of selfing rate and locus-specific mutation rates for a partially selfing population

We present a Bayesian method for characterizing the mating system of populations reproducing through a mixture of self-fertilization and random outcrossing. Our method uses patterns of genetic variation across the genome as a basis for inference about pure hermaphroditism, androdioecy, and gynodioecy. We extend the standard coalescence model to accommodate these mating systems, accounting explicitly for multilocus identity disequilibrium, inbreeding depression, and variation in fertility among mating types. We incorporate the Ewens Sampling Formula (ESF) under the infinite-alleles model of mutation to obtain a novel expression for the likelihood of mating system parameters. Our Markov chain Monte Carlo (MCMC) algorithm assigns locus-specific mutation rates, drawn from a common mutation rate distribution that is itself estimated from the data using a Dirichlet Process Prior (DPP) model. Among the parameters jointly inferred are the population-wide rate of self-fertilization, locus-specific mutation rates, and the number of generations since the most recent outcrossing event for each sampled individual

Why we (usually) don't have to worry about multiple comparisons

Applied researchers often find themselves making statistical inferences in settings that would seem to require multiple comparisons adjustments. We challenge the Type I error paradigm that underlies these corrections. Moreover we posit that the problem of multiple comparisons can disappear entirely when viewed from a hierarchical Bayesian perspective. We propose building multilevel models in the settings where multiple comparisons arise. Multilevel models perform partial pooling (shifting estimates toward each other), whereas classical procedures typically keep the centers of intervals stationary, adjusting for multiple comparisons by making the intervals wider (or, equivalently, adjusting the $p$-values corresponding to intervals of fixed width). Thus, multilevel models address the multiple comparisons problem and also yield more efficient estimates, especially in settings with low group-level variation, which is where multiple comparisons are a particular concern

Why we (usually) don't have to worry about multiple comparisons

This is an Accepted Manuscript of an article published by Taylor & Francis Group in Journal Of Research On Educational Effectiveness on 04/03/2012, available online: https://doi.org/10.1080/19345747.2011.618213Applied researchers often find themselves making statistical inferences in settings that would seem to require multiple comparisons adjustments. We challenge the Type I error paradigm that underlies these corrections. Moreover we posit that the problem of multiple comparisons can disappear entirely when viewed from a hierarchical Bayesian perspective. We propose building multilevel models in the settings where multiple comparisons arise. Multilevel models perform partial pooling (shifting estimates toward each other), whereas classical procedures typically keep the centers of intervals stationary, adjusting for multiple comparisons by making the intervals wider (or, equivalently, adjusting the p values corresponding to intervals of fixed width). Thus, multilevel models address the multiple comparisons problem and also yield more efficient estimates, especially in settings with low group-level variation, which is where multiple comparisons are a particular concern

Some Issues in Using Sign Restrictions for Identifying Structural VARs

The paper looks at estimation of structural VARs with sign restrictions. Since sign restrictions do not generate a unique model it is necessary to find some way of summarizing the information they yield. Existing methods present impulse responses from different models and it is argued that they should come from a common model. If this is not done the implied shocks implicit in the impulse responses will not be orthogonal. A method is described that tries to resolve this difficulty. It works with a common model whose impulse responses are as close as possible to the median values of the impulse responses (taken over the range of models satisfying the sign restrictions). Using a simple demand and supply model it is shown that there is no reason to think that sign restrictions will generate better quantitative estimates of the effects of shocks than existing methods such as assuming a system is recursive.