General N-th Degree Stochastic Dominance

This paper examines N-th degree stochastic dominance which is used to compare the risk factor of risky assets after summarizing the definitions of first degree stochastic dominance and second degree stochastic dominance. The paper defines general N-th degree stochastic dominance, presents a sufficient and necessary condition which is the equivalent theorem of general N-th degree stochastic dominance. The feasible utility form is constructed to explain the economic meaning of N-th degree stochastic dominance in the field of financial economics. The equivalent condition is described by the probability distribution functions of risky assets, which are not related to utility functions (preference relations).

Testing against second-order stochastic dominance of multiple distributions

Second-order stochastic dominance plays an important role in reliability and various branches of economics such as finance and decision-making under risk, and statistical testing for the stochastic dominance is often useful in practice. In this paper, we present a test of stochastic equality under the constraint of second-order stochastic dominance based on the theory of empirical processes. The asymptotic distribution of the test statistic is obtained, and a simple method to compute the critical value is derived. Simulation results and real data examples are presented to illustrate the proposed test method.

CONVEX CONCENTRATION INEQUALITIES FOR CONTINUOUS GAS AND STOCHASTIC DOMINATION

In this article, we consider the continuous gas in a bounded domain ∧ of R^＋ or R^d described by a Gibbsian probability measure μη∧ associated with a pair interaction φ, the inverse temperature β, the activity z 〉 0, and the boundary condition η. Define F ∫ωf（s）wA（ds）. Applying the generalized Ito＇s formula for forward-backward martingales （see Klein et M. [5]）, we obtain convex concentration inequalities for F with respect to the Gibbs measure μη∧. On the other hand, by FKG inequality on the Poisson space, we also give a new simple argument for the stochastic domination for the Gibbs measure.

Analyzing multidimensional measures of poverty and their influences in China's Qinba Mountains

We use the Alkire–Foster poverty measure and decomposition method to study multidimensional poverty in the Qinling–Daba contiguous poor area of China's Henan Province.We examine absolute,relative,and multidimensional poverty focusing on heads of household and family characteristics as constituents of escaping each.We find that the multidimensional poverty index declines to a low level as values of k increase.Combining first-order random dominance with second-order stochastic dominance quickly determines rankings in the multidimensional poverty index.Increasing non-agricultural income emerges as the most important influence on escaping rural poverty,whereas households with elderly and children are at greatest risk for falling into poverty.

Estimation of Ordered Means of Two Normal Distributions with Ordered Variances

The authors consider the problem of estimating the ordered means of two normal distributions with unknown ordered variances. The authors discuss the estimation of two ordered means, individually, in terms of stochastic domination and MSE （mean squared error）. The authors show that in estimating the mean with larger variance, the usual estimator under order restriction on means can be improved upon. However, in estimating the mean with smaller variance, the usual estimator can＇t be improved upon even under MSE. The authors also discuss simultaneous estimation problem of two ordered means when unknown variances are ordered.

On the strong convergence properties for weighted sums of negatively orthant dependent random variables

In the paper, the strong convergence properties for two different weighted sums of negatively orthant dependent(NOD) random variables are investigated. Let {X, n ≥ 1}be a sequence of NOD random variables. The results obtained in the paper generalize the corresponding ones for i.i.d. random variables and identically distributed NA random variables to the case of NOD random variables, which are stochastically dominated by a random variable X. As a byproduct, the Marcinkiewicz-Zygmund type strong law of large numbers for NOD random variables is also obtained.

A Class of Random Approximation Theorems for Random Sums of Arbitrary Stochastic Sequence on Nonhomogeneous Markov Chains

In this paper, the notion of limit random logarithmic likelihood ratio of stochastic sequence, as a measure of dissimilarity between the joint distribution on measure P and the Markov distribution on measure Q, is introduced. A class of random approximation theorems for arbitrary stochastic dominated sequence are obtained by using the tools of generating functions and the tailed-probability generating functions.

Discovering admissible Web services with uncertain QoS

Open and dynamic environments lead to inher- ent uncertainty of Web service QoS （Quality of Service）, and the QoS-aware service selection problem can be looked upon as a decision problem under uncertainty. We use an empiri- cal distribution function to describe the uncertainty of scores obtained from historical transactions. We then propose an approach to discovering the admissible set of services in- cluding alternative services that are not dominated by any other alternatives according to the expected utility criterion. Stochastic dominance （SD） rules are used to compare two services with uncertain scores regardless of the distribution form of their uncertain scores. By using the properties of SD rules, an algorithm is developed to reduce the number of SD tests, by which the admissible services can be reported pro- gressively. We prove that the proposed algorithm can be run on partitioned or incremental alternative services. Moreover, we achieve some useful theoretical conclusions for correct pruning of unnecessary calculations and comparisons in each SD test, by which the efficiency of the SD tests can be im- proved. We make a comprehensive experimental study using real datasets to evaluate the effectiveness, efficiency, and scal- ability of the proposed algorithm.

Mate choice decisions by searchers

For more than two decades rudimentary versions of the fixed sample and sequential search strategies have provided the primary theoretical foundation for the study of mate choice decisions by searchers. The theory that surrounds these models has expanded markedly over this time period. In this paper, we review and extend results derived from these models, with a focus on the empirical analysis of searcher behavior. The basic models are impractical for empirical purposes because they rely on the as- sumption that searchers--and, for applied purposes, researchers--assess prospective mates based on their quality, the fitness consequences of mate choice decisions. Here we expound versions of the models that are more empirically useful, reformulated to reflect decisions based on male phenotypic characters. For some organisms, it may be possible to use preference functions to de- rive predictions from the reformulated models and thereby avoid difficulties associated with the measurement of male quality per se. But predictions derived from the two models are difficult to differentiate empirically, regardless of how the models are formu- lated. Here we develop ideas that illustrate how this goal might be accomplished. In addition, we clarify how the variability of male quality should be evaluated and we extend what is known about how this variability influences searcher behavior under each model. More general difficulties associated with the empirical study of mate choice decisions by searchers are also discussed [Current Zoology 59 （2）： 184-199, 2013].

A New Criterion for Environmental Risk Management of Multiplication Processes

This paper aims to propose ERT （Expected Reaching Time）, a new risk adverse evaluation criterion of finite multiplication processes, and to examine its properties in relation to the dominance criterion. The ERT means the expected time that takes for an objective valiable to reach a target value. To deal with the environmental risk involved in the process, the expectation maximizing strategy may be the most well known. However, for many cases the dominance strategy rather than the expectation maximizing strategy is adopted and works very well. In this paper we first prove rigorously that minimization of the ERT is equivalent to the dominance criterion in the infinite period. Then we demonstrate by simulation that the ERT gives almost equal evaluation as the dominance criterion even for the finite multiplications, after showing that it is approximately proportional to the logarithm of the target value.