On multivariate quantiles under partial orders

This paper focuses on generalizing quantiles from the ordering point of view. We propose the concept of partial quantiles, which are based on a given partial order. We establish that partial quantiles are equivariant under order-preserving transformations of the data, robust to outliers, characterize the probability distribution if the partial order is sufficiently rich, generalize the concept of efficient frontier, and can measure dispersion from the partial order perspective. We also study several statistical aspects of partial quantiles. We provide estimators, associated rates of convergence, and asymptotic distributions that hold uniformly over a continuum of quantile indices. Furthermore, we provide procedures that can restore monotonicity properties that might have been disturbed by estimation error, establish computational complexity bounds, and point out a concentration of measure phenomenon (the latter under independence and the componentwise natural order). Finally, we illustrate the concepts by discussing several theoretical examples and simulations. Empirical applications to compare intake nutrients within diets, to evaluate the performance of investment funds, and to study the impact of policies on tobacco awareness are also presented to illustrate the concepts and their use.Comment: Published in at http://dx.doi.org/10.1214/10-AOS863 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Multivariate concave and convex stochastic dominance

Stochastic dominance permits a partial ordering of alternatives (probability distributions on consequences) based only on partial information about a decision maker’s utility function. Univariate stochastic dominance has been widely studied and applied, with general agreement on classes of utility functions for dominance of different degrees. Extensions to the multivariate case have received less attention and have used different classes of utility functions, some of which require strong assumptions about utility. We investigate multivariate stochastic dominance using a class of utility functions that is consistent with a basic preference assumption, can be related to well-known characteristics of utility, and is a natural extension of the stochastic order typically used in the univariate case. These utility functions are multivariate risk averse, and reversing the preference assumption allows us to investigate stochastic dominance for utility functions that are multivariate risk seeking. We provide insight into these two contrasting forms of stochastic dominance, develop some criteria to compare probability distributions (hence alternatives) via multivariate stochastic dominance, and illustrate how this dominance could be used in practice to identify inferior alternatives. Connections between our approach and dominance using different stochastic orders are discussed.decision analysis: multiple criteria, risk; group decisions; utility/preference: multiattribute utility, stochastic dominance, stochastic orders

Risk Sharing and Group Decision Making

In a decision-making problem where a group will receive an uncertain payoff which must be divided among the members of the group, the ultimate payoff of interest is the vector of individual payoffs received by the members of the group. In this paper, preferences are quantified in terms of cardinal utility functions for such vectors of payoffs. These utility functions can represent preferences concerning “equitable” and “inequitable” vectors of payoffs as well as attitudes toward risk. The individual utility functions are aggregated to form a group utility function for the vector of payoffs, and this latter function is, in turn, used to generate a group utility function for the overall group payoff and a sharing rule for dividing the group payoff into individual payoffs. The resulting group decisions are Pareto optimal in utility space. Properties of the sharing rule and the group utility function are investigated for additive and multilinear group utility functions

Different roles of similarity and predictability in auditory stream segregation

Sound sources often emit trains of discrete sounds, such as a series of footsteps. Previously, two dif¬ferent principles have been suggested for how the human auditory system binds discrete sounds to¬gether into perceptual units. The feature similarity principle is based on linking sounds with similar characteristics over time. The predictability principle is based on linking sounds that follow each other in a predictable manner. The present study compared the effects of these two principles. Participants were presented with tone sequences and instructed to continuously indicate whether they perceived a single coherent sequence or two concurrent streams of sound. We investigated the influence of separate manipulations of similarity and predictability on these perceptual reports. Both grouping principles affected perception of the tone sequences, albeit with different characteristics. In particular, results suggest that whereas predictability is only analyzed for the currently perceived sound organization, feature similarity is also analyzed for alternative groupings of sound. Moreover, changing similarity or predictability within an ongoing sound sequence led to markedly different dynamic effects. Taken together, these results provide evidence for different roles of similarity and predictability in auditory scene analysis, suggesting that forming auditory stream representations and competition between alter¬natives rely on partly different processes

Academic Development of First-Year Living-Learning Program Students before and after Hurricanes Katrina and Rita of 2005

Previous research suggests that the far-reaching impacts of hurricanes include the academic performance of students. In an examination of such impacts, we found a trend toward self-perceived decline in some performance indicators relative to students at peer universities. However, few longitudinal impacts were found, perhaps because of the sense of community offered by the living-learning program. These results may inform administrators and faculty of areas for emphasis in mitigating future impacts. Robert V. Rohli is a Professor of Geography and Faculty Director of the Residential Colleges Program at Louisiana State University in Baton Rouge, LA. Kurt J. Keppler is Vice Chancellor for Student Life & Enrollment at Louisiana State University. Daniel L. Winkler is a Graduate Assistant at Louisiana State University

Pennsylvania Folklife Vol. 21, No. 4

• The Herr and Zeller Houses • Pennsylvania German Astronomy and Astrology II: The Moon • Travel Journals as a Folklife Research Tool: Impressions of the Pennsylvania Germans • My Interview with a Powwower • American Emigrants from the Territories of the Bishropric of Speyer • Emigrants to America from the Duchy of Zweibrucken • Funeral Customs: Folk-Cultural Questionnaire No. 24https://digitalcommons.ursinus.edu/pafolklifemag/1048/thumbnail.jp

Scoring rules in probability assessment and evaluation

The purpose of this paper is to briefly discuss some important current questions and problems related to the use of scoring rules (SRs) both in connection with the actual assessment of probabilities and with the evaluation of probability forecasts and probability assessors. With regard to the assessment process, we consider both the case in which the assessor's utility function is linear and the case in which his utility function is nonlinear. Under linear utility, important problems of concern are the sensitivity of SRs to deviations from optimality (with a strictly proper SR, optimality consists of the assessor making his statements correspond to his judgments) and the effect of psychological considerations arising from the use of different SRs. Under nonlinear utility, SRs should be modified to allow for the nonlinearity in such a manner that for a specific utility function, the modified SRs are strictly proper. This introduces the difficult question of the assessment of the assessor's utility function. With regard to the evaluation process (as opposed to the assessment process), we consider the process from an inferential viewpoint and from a decision-theoretic viewpoint. From an inferential viewpoint, attributes such as validity may be of interest, and in certain circumstances these attributes may be related to SRs. The attributes of interest, of course, depend on the framework within which the evaluation process is undertaken. From a decision-theoretic viewpoint, SRs may be related to a decision maker's utilities or expected utilities (under uncertainty about the utilities) if the decision maker uses the assessed probabilities in an actual decision situation.In summary, there are many important questions and problems related to SRs, and the need for future research on these problems seems clear. Such research should lead to a greatly improved understanding of the processes of probability assessment and evaluation.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/32842/1/0000218.pd