15,594 research outputs found
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
Partial stochastic dominance for the multivariate Gaussian distribution
Gaussian comparison inequalities provide a way of bounding probabilities
relating to multivariate Gaussian random vectors in terms of probabilities of
random variables with simpler correlation structures. In this paper, we
establish the partial stochastic dominance result that the cumulative
distribution function of the maximum of a multivariate normal random vector,
with positive intraclass correlation coefficient, intersects the cumulative
distribution function of a standard normal random variable at most once. This
result can be applied to the Bayesian design of a clinical trial in which
several experimental treatments are compared to a single control.Comment: 7 page
Conditional stochastic dominance tests in dynamic settings
This paper proposes nonparametric consistent tests of conditional stochastic dominance of arbitrary order in a dynamic setting. The novelty of these tests resides on the nonparametric manner of incorporating the information set into the test. The test allows for general forms of unknown serial and mutual dependence between random variables, and has an asymptotic distribution under the null hypothesis that can be easily approximated by a p-value transformation method. This method has a good finite-sample performance. These tests are applied to determine investment efficiency between US industry portfolios conditional on the performance of the market portfolio. Our analysis suggests that Utilities are the best performing sectors in normal as well as distress episodes of the market.Empirical processes, Hypothesis testing, Lower partial moments, Martingale difference sequence, P-value transformation, Stochastic dominance,
Partial Multidimensional Inequality Orderings
The paper investigates how comparisons of multivariate inequality can be made robust to varying the intensity of focus on the share of the population that are more relatively deprived. It follows the dominance approach to making inequality comparisons, as developed for instance by Atkinson (1970), Foster and Shorrocks (1988) and Formby, Smith, and Zheng (1999) in the unidimensional context, and Atkinson and Bourguignon (1982) in the multidimensional context. By focusing on those below a multidimensional inequality “frontier”, we are able to reconcile the literature on multivariate relative poverty and multivariate inequality. Some existing approaches to multivariate inequality actually reduce the distributional analysis to a univariate problem, either by using a utility function first to aggregate an individual’s multiple dimensions of well-being, or by applying a univariate inequality analysis to each dimension independently. One of our innovations is that unlike previous approaches, the distribution of relative well-being in one dimension is allowed to affect how other dimensions influence overall inequality. We apply our approach to data from India and Mexico using monetary and non-monetary indicators of well-being.Inequality, multidimensional comparisons, stochastic dominance
Statistical Inference on Stochastic Dominance Efficiency. Do Omitted Risk Factors Explain the Size and Book-to-Market Effects?
This paper discusses statistical inference on the second-orderstochastic dominance (SSD) efficiency of a given portfolio relative toall portfolios formed from a set of assets. We derive the asymptoticsampling distribution of the Post test statistic for SSD efficiency.Unfortunately, a test procedure based on this distribution involveslow power in small samples. Bootstrapping is a more powerful approachto sampling error. We use the bootstrap to test if the Fama and Frenchvalue-weighted market portfolio is SSD efficient relative to benchmarkportfolios formed on market capitalization and book-tomarket equityratio. During the late 1970s and during the 1980s, the marketportfolio is significantly SSD inefficient, even if we use samples ofonly 60 monthly observations. This suggests that the size andbook-to-market effects cannot be explained by omitted risk factorslike higher-order central moments or lower partial moments.market efficiency;asset pricing;stochastic dominance;size and book-to-market effects;statistical inference
Testing for the Monotone Likelihood Ratio Assumption
Monotonicity of the likelihood ratio for conditioned densities is a common technical assumption in economic models. But we have found no empirical tests for its plausibility. This paper develops such a test based on the theory of order-restricted inference, which is robust with respect to the correlation structure of the distributions being compared. We apply the test to study the technology revealed by agricultural production experiments. For the data under scrutiny, the results support the assumption of the monotone likelihood ratio. In a second application, we find some support for the assumption of affiliation among bids cast in a multiple-round Vickrey auction for a consumption good. Keywords: affiliation, auction, likelihood ratio, order-restricted inference, stochastic order.
Multidimensional Poverty Dominance: Statistical Inference and an Application to West Africa
This paper tests for robust multidimensional poverty comparisons across six countries of the West African Economic and Monetary Union (WAEMU). Two dimensions are considered, nutritional status and assets. The estimation of the asset index is based on two factorial analysis methods. The first method uses Multiple Correspondence Analysis; the second is based on the maximization of a likelihood function and on bayesian analysis. Using Demographic and Health Surveys (DHS), pivotal bootstrap tests lead to statistically significant dominance relationships between 12 of the 15 possible pairs of the six WAEMU countries. Multidimensional poverty is also inferred to be more prevalent in rural than in urban areas. These results tend to support those derived from more restrictive unidimensional dominance tests.Stochastic dominance, factorial analysis, bayesian analysis, multidimensional poverty, empirical likelihood function, bootstrap tests
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Testing Downside Risk Efficiency Under Market Distress
In moments of distress downside risk measures like Lower Partial Moments (LPM) are more appropriate than the standard variance to characterize risk. The goal of this paper is to study how to compare portfolios in these situations. In order to do that we show the close connection between mean-risk effciency sets and stochastic dominance under distress episodes of the market, and use the latter property to propose a hypothesis test to discriminate between portfolios across risk aversion levels. Our novel family of test statistics for testing stochastic dominance under distress makes allowance for testing orders of dominance higher than zero, for general forms of dependence between portfolios and can be extended to residuals of regression models. These results are illustrated in the empirical application for data from US stocks. We show that mean-variance strategies are stochastically dominated by mean-risk efficient sets in episodes of financial distress
Testing for Bivariate Stochastic Dominance Using Inequality Restrictions
In this paper, we propose of a test of bivariate stochastic dominance using a generalized framework for testing inequality constraints. Unlike existing tests, this test has the advantage of utilizing the covariance structure of the estimates of the joint distribution functions. The performance of our proposed test is examined by way of a Monte Carlo experiment. We also consider an empirical example which utilizes household survey data on income and health status.Stochastic dominance, inequality restrictions, multidimensional welfare
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