Some remarks on stochastic dominance

The present work proposes a definition of dominance (dominance in the strict sense), which is weaker than first order stochastic dominance, stating precisely that the r.v.Y dominatesX (XY) if Pr(YX)=1.Such a dominance in the strict sense is then compared with first and second order stochastic dominance and with dominance between descisions of the same decision problem summarised in a table of results, arriving at certain general remarks about decision problems and the choice between r.v.'s. Indications are also given about how it is possible to obtain simple and useful bounds for Pr(YX).

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Riassunto Nel presente lavoro si propone una definizione di dominanza (dominanza in senso stretto) più debole della dominanza stocastica del prim'ordine, precisamente dicendo che la v.a.Y dominaX (XY) se Pr(YX)=1.Si confronta poi tale dominanza in senso stretto con le dominanze stocastiche del primo e del secondo ordine e con la dominanza tra decisioni di uno stesso problema di decisione sintetizzato in una tabella dei risultati giungendo ad alcune precisazioni generali sui problemi di decisione e di scelta tra v.a. Si danno anche indicazioni su come sia possibile ottenere limitazioni per la Pr(YX).

     

Testing for stochastic dominance using the weighted McFadden-type statistic

We demonstrate that when testing for stochastic dominance of order three and above, using a weighted version of the Kolmogorov–Smirnov-type statistic proposed by McFadden [1989. In: Fomby, T.B., Seo, T.K. (Eds.), Studies in the Economics of Uncertainty. Springer, New York, pp. 113–134] is necessary for obtaining a non-degenerate asymptotic distribution. Since the asymptotic distribution is complex, we discuss a bootstrap approximation for it in the context of a real application.     

An improved bootstrap test of stochastic dominance

We propose a new method of testing stochastic dominance that improves on existing tests based on the standard bootstrap or subsampling. The method admits prospects involving infinite as well as finite dimensional unknown parameters, so that the variables are allowed to be residuals from nonparametric and semiparametric models. The proposed bootstrap tests have asymptotic sizes that are less than or equal to the nominal level uniformly over probabilities in the null hypothesis under regularity conditions. This paper also characterizes the set of probabilities so that the asymptotic size is exactly equal to the nominal level uniformly. As our simulation results show, these characteristics of our tests lead to an improved power property in general. The improvement stems from the design of the bootstrap test whose limiting behavior mimics the discontinuity of the original test’s limiting distribution.     

Stochastic dominance efficient sets and stochastic spanning

Decisions in Economics and Finance - We derive sufficient conditions for non-emptiness of the efficient sets for stochastic dominance relations, usually employed in economics and finance. We do so...     

A note on portfolio selection and stochastic dominance

This note provides new and simpler conditions ensuring that, when one portfolio dominates another via stochastic dominance, a decision maker prefers the first one. The conditions are derived for the case of third-order stochastic dominance and for the general case of Nth-order stochastic dominance.     

Partial identification of probability distributions with misclassified data

This paper addresses the problem of data errors in discrete variables. When data errors occur, the observed variable is a misclassified version of the variable of interest, whose distribution is not identified. Inferential problems caused by data errors have been conceptualized through convolution and mixture models. This paper introduces the direct misclassification approach. The approach is based on the observation that in the presence of classification errors, the relation between the distribution of the ‘true’ but unobservable variable and its misclassified representation is given by a linear system of simultaneous equations, in which the coefficient matrix is the matrix of misclassification probabilities. Formalizing the problem in these terms allows one to incorporate any prior information into the analysis through sets of restrictions on the matrix of misclassification probabilities. Such information can have strong identifying power. The direct misclassification approach fully exploits it to derive identification regions for any real functional of the distribution of interest. A method for estimating the identification regions and construct their confidence sets is given, and illustrated with an empirical analysis of the distribution of pension plan types using data from the Health and Retirement Study.     

Bayesian clustering of distributions in stochastic frontier analysis

In stochastic frontier analysis, firm-specific efficiencies and their distribution are often main variables of interest. If firms fall into several groups, it is natural to allow each group to have its own distribution. This paper considers a method for nonparametrically modelling these distributions using Dirichlet processes. A common problem when applying nonparametric methods to grouped data is small sample sizes for some groups which can lead to poor inference. Methods that allow dependence between each group’s distribution are one set of solutions. The proposed model clusters the groups and assumes that the unknown distribution for each group in a cluster are the same. These clusters are inferred from the data. Markov chain Monte Carlo methods are necessary for model-fitting and efficient methods are described. The model is illustrated on a cost frontier application to US hospitals.     

Probabilistic sophistication,second order stochastic dominance and uncertainty aversion

We study the interplay of probabilistic sophistication, second order stochastic dominance and uncertainty aversion, three fundamental notions in choice under uncertainty. In particular, our main result, Theorem 2, characterizes uncertainty averse preferences that are probabilistically sophisticated, as well as uncertainty averse preferences that satisfy second order stochastic dominance. As a byproduct, Proposition 2 highlights a fundamental tension between probabilistic sophistication/second order stochastic dominance and uncertainty aversion in the presence of nontrivial unambiguous events.     

Roots and effects of financial misperception in a stochastic dominance framework

This work deals with the issue of investors’ irrational behavior and financial products’ misperception. The theoretical analysis of the mechanisms driving erroneous assessment of investment performances is explored. The study is supported by the application of Monte Carlo simulations to the remarkable case of structured financial products. Some motivations explaining the popularity of these complex financial instruments among retail investors are also provided. In particular, investors are assumed to compare the performances of different projects through stochastic dominance rules. Unreasonably and in contrast with results obtained by the application of the selected criteria, investors prefer complex securities to standard ones. In this paper, introducing a new definition for stochastic dominance which presents asymmetric property, we provide theoretical and numerical results showing how investors distort stochastic returns and make questionable investment choices. Results are explained in terms of framing and representative effects, which are behavioral finance type arguments showing how decisions may depend on the way the available alternatives are presented to investors.     

Characterizations of probability distributions via bivariate regression of record values

Bairamov et al. (Aust N Z J Stat 47:543–547, 2005) characterize the exponential distribution in terms of the regression of a function of a record value with its adjacent record values as covariates. We extend these results to the case of non-adjacent covariates. We also consider a more general setting involving monotone transformations. As special cases, we present characterizations involving weighted arithmetic, geometric, and harmonic means.     

Testing for infinite order stochastic dominance with applications to finance, risk and income inequality

In this paper we develop a test of infinite order degree stochastic dominance based on the use of the empirical Laplace transform function. Two applications are considered. One uses the income data of Anderson (Econometrica 64:1183–1193, 1996) and derives results consistent with his. In the other application we examine the dominance between the U.S. and U.K. stock markets. Using data on the S&P 500 and the FTALL-Share we show that the U.S. displays infinite order degree stochastic dominance of the U.K.

A note on the assumed distributions in stochastic frontier models

Stochastic frontier models all need an assumption on the distributional form of the (in)efficiency component. Generally this efficiency component is assumed to be half normally, truncated normally, or exponentially distributed. This paper shows that the exponential distribution is, just like the half normal distribution, a special case of the truncated normal distribution. Moreover, this paper discusses the implications that this finding has on estimation.     

Load and no-load mutual fund dynamics during the 1987 market crash: A stochastic dominance analysis

Using a large sample of equity mutual fund returns, we compare performance of load and no-load funds during the 1987 crash. Differences in return distributions, particularly in the higher moments when the market was under stress, suggest a greater use of portfolio insurance by no-load fund managers. Using stochastic dominance, we find that load and no-load funds performed equally well before the crash. No-load returns dominated load fund returns during the crash. Load fund returns dominate after the crash. Over the entire month, no-load funds dominate. We attribute this to investor behavior motivated by the lack of a front-end load.     

Performance measurement and best-practice benchmarking of mutual funds: combining stochastic dominance criteria with data envelopment analysis

We propose a method for mutual fund performance measurement and best-practice benchmarking, which endogenously identifies a dominating benchmark portfolio for each evaluated mutual fund. Dominating benchmarks provide information about efficiency improvement potential as well as portfolio strategies for achieving them. Portfolio diversification possibilities are accounts for by using Data Envelopment Analysis (DEA). Portfolio risk is accounted for in terms of the full return distribution by utilizing Stochastic Dominance (SD) criteria. The approach is illustrated by an application to US based environmentally responsible mutual funds.