Stochastic Dominance Research Articles

Simultaneous marginal homogeneity versus directional alternatives for multivariate binary data with application to circular economy assessments

AbstractCommodity price volatility is a major source of instability in those countries that are primarily commodity‐dependent and has a negative impact, especially on economic growth. With this premise, commodities represent an effective financial exchange tool that nowadays finds relevance in being involved in the processes inherent to environmental sustainability. This work focus on raw materials and their demand, connected with the need for a transition towards the Circular Economy, as part of a strategy to address commodity supply disruptions. It presupposes changes in the mentality and behavior of companies in the various economic sectors. A crucial issue debated in the literature concerns whether or not the size of the companies favors their attitude towards Circular Economy. We propose a nonparametric method to test the effect of firm size on their propensity to undertake Circular Economy activities. Considering of such activities, this propensity is a multidimensional concept and it can be represented by a ‐dimensional vector of proportions. Each element of the vector represents the share of companies of the population under study that implement a specific Circular Economy activity. The main difficulty of such a multivariate testing problem, together with the multidimensional nature of the dichotomous response, is the one‐sided type alternative, which is a stochastic dominance for multidimensional binary variables. A Monte Carlo simulation study proves the good power behavior of the proposed solution, based on a nonparametric approach. Case studies related to Italian small and medium enterprises in some strategic sectors are also addressed.

Statistical decision theory respecting stochastic dominance

The statistical decision theory pioneered by (Wald, Statistical decision functions, Wiley, 1950) has used state-dependent mean loss (risk) to measure the performance of statistical decision functions across potential samples. We think it evident that evaluation of performance should respect stochastic dominance, but we do not see a compelling reason to focus exclusively on mean loss. We think it instructive to also measure performance by other functionals that respect stochastic dominance, such as quantiles of the distribution of loss. This paper develops general principles and illustrative applications for statistical decision theory respecting stochastic dominance. We modify the Wald definition of admissibility to an analogous concept of stochastic dominance (SD) admissibility, which uses stochastic dominance rather than mean sampling performance to compare alternative decision rules. We study SD admissibility in two relatively simple classes of decision problems that arise in treatment choice. We reevaluate the relationship between the MLE, James–Stein, and James–Stein positive part estimators from the perspective of SD admissibility. We consider alternative criteria for choice among SD-admissible rules. We juxtapose traditional criteria based on risk, regret, or Bayes risk with analogous ones based on quantiles of state-dependent sampling distributions or the Bayes distribution of loss.

Consensus reaching with heterogeneous stochastic dominance in the enterprise credit rating under linguistic distribution assessments context

Consensus reaching with heterogeneous stochastic dominance in the enterprise credit rating under linguistic distribution assessments context

Multivariate Almost Stochastic Dominance: Transfer Characterizations and Sufficient Conditions Under Dependence Uncertainty

Decision with Several Objectives Under Uncertainty Important decisions typically involve multiple objectives and uncertainty. Assessing both multivariate utility and multivariate distributions for the attributes can be challenging. Moreover, big decisions are usually made by boards or committees with members holding divergent views and preferences and facing pressures from different stakeholders. Thus, a full-blown traditional decision analysis that leads to the computation of expected utility is very difficult at best and often not possible. In “Multivariate Almost Stochastic Dominance: Transfer Characterizations and Sufficient Conditions Under Dependence Uncertainty” Müller, Scarsini, Tsetlin, and Winkler develop sufficient conditions for multivariate almost stochastic dominance based on marginal distributions of the attributes or just on their means and variances. Such tools, consistent with normative decision analysis, are useful when making important decisions in today’s fast-moving and often complex world.

Inference on Consensus Ranking of Distributions

Instead of testing for unanimous agreement, I propose learning how broad of a consensus favors one distribution over another (of earnings, productivity, asset returns, test scores, etc.). Specifically, given a sample from each of two distributions, I propose statistical inference methods to learn about the set of utility functions for which the first distribution has higher expected utility than the second distribution. With high probability, an “inner” confidence set is contained within this true set, while an “outer” confidence set contains the true set. Such confidence sets can be formed by inverting a proposed multiple testing procedure that controls the familywise error rate. Theoretical justification comes from empirical process results, given that very large classes of utility functions are generally Donsker (subject to finite moments). The theory additionally justifies a uniform (over utility functions) confidence band of expected utility differences, as well as tests with a utility-based “restricted stochastic dominance” as either the null or alternative hypothesis. Simulated and empirical examples illustrate the methodology.

Testing higher and infinite degrees of stochastic dominance for small samples: A Bayesian approach

This study proposes a distribution-free Bayesian procedure that detects infinite degrees of stochastic dominance (SD∞) between two random outcomes and then seeks a finite degree k≥1 of stochastic dominance (SDk). Based on small samples, we construct four-choice Bayesian tests by combining an encompassing prior Bayesian model with the Dirichlet process priors that discriminate between SD∞ and SDk of one random variable over the other with non-dominance or equality between them. We use Monte Carlo simulations to evaluate the novel Bayesian tests for SDk and SD∞ and compare them to the subsampling and bootstrap significance tests for SDk. Our simulation shows that the Bayesian tests for SDk outperform the significance tests for small samples, especially for detecting non-stochastic dominance. This study shows that the test for SD∞ is an accurate decision-making tool when using small samples.

Regret theory, Allais’ paradox, and Savage’s omelet

We study a sufficiently general regret criterion for choosing between two probabilistic lotteries. For independent lotteries, the criterion is consistent with stochastic dominance and can be made transitive by a unique choice of the regret function. Together with additional (and intuitively meaningful) super-additivity property, the regret criterion resolves the Allais’ paradox including the cases were the paradox disappears, and the choices agree with the expected utility. This super-additivity property is also employed for establishing consistency between regret and stochastic dominance for dependent lotteries. Furthermore, we demonstrate how the regret criterion can be used in Savage’s omelet, a classical decision problem in which the lottery outcomes are not fully resolved. The expected utility cannot be used in such situations, as it discards important aspects of lotteries.

A Multi-Stage Model for Perceived Quality Evaluation of Clothing Brands

Perceived quality is crucial for the functioning of clothing brands. However, accurate evaluation of the perceived quality of clothing brands remains a common challenge. To achieve a multidimensional evaluation of the perceived quality of clothing brands, an index system is derived based on perceived quality theory. Then, by combining a fine-grained sentiment analysis approach with stochastic dominance criteria, a multi-stage model ECRM is proposed for the perceived quality evaluation of clothing brands based on online user reviews. ECRM comprises three stages: Extraction, Classification, and Ranking. To begin with, Contrastive Attention and dependency parsing are used to extract attribute–viewpoint phrases from online reviews. Subsequently, the pre-trained models are employed to classify the indexes and sentiment levels of these phrases. Furthermore, the perceived quality indexes are ranked using stochastic dominance criteria and the PROMETHEE-II method. Empirical analysis is conducted for the clothing brands of ALDB, AND, BNL, and QPL; the results show that, based on online user reviews, ECRM enables accurate evaluation of the perceived quality of clothing brands. Based on the evaluation results, it is found that Comfort, External, Protection, and Fineness are highly valued by consumers; moreover, the four brands focus on different indexes. Specific strategies for perceived quality improvements are proposed depending on the current status of the brands.

Green Certificate-Driven Photovoltaic Promotion in Distribution Networks Hosting Hydrogen Fueling Stations for Future Sustainable Transportation: A Risk-Adjusted Dominance Analysis

The growing number of hydrogen vehicles (HVs) has necessitated the development of hydrogen fueling stations (HFSs) to meet the hydrogen demand. This development will target environmental concerns related to electricity generation as HFSs consume power to convert electricity into hydrogen. This study focuses on the optimal risk-aware scheduling problem of a distributed network highly penetrated with photovoltaic (PV) resources. The model addresses the optimal operation of HFs under time-of-use, demand response, and multi-market mechanisms with an expanded role for PV generation under the green certificate (GCT) approach. This brings further environmental and economic benefits, as there is a growing global emphasis on the shift to a low-carbon economy. However, the uncertainties arising from PV operation, HVs’ demand, electricity load, and market prices, potentially affect the decision-maker's ability under the risky conditions. Though second-order stochastic dominance (STD) is implemented for risk management. Results show that applying the GCT method increases 5% (from 0.52 to 0.61 MW) of renewable generation and reduces 23% (300 kg) of CO2 emissions. As the conservativity of decision-makers enhances, 10% of further operation costs are imposed on the system. Results indicate that next to curbing CO2 emissions, the flexibility and robustness of the system can be improved.

СТОХАСТИЧЕСКОЕ ДОМИНИРОВАНИЕ В АКЦИЯХ ИННОВАЦИОННЫХ КОМПАНИЙ НА РОССИЙСКОМ ФОНДОВОМ РЫНКЕ

During the period of significant economic changes, the role of the state in the economy is strengthening, while the need for efficient resource allocation remains, which is characteristic of the market mechanism. The criterion for determining preferences based on second-order stochastic dominance, considered in the paper, allows the planner to identify the most preferred innovative companies for conducting appropriate policies. The result of the study is a hierarchy of preferences for a set of innovative companies represented on the Russian stock market. The article presents a calculation algorithm for series of different lengths generated by a stochastic process. An overview of the organized capital market for innovative companies is presented.

Permutation tests for multivariate order-constrained testing problems

This article discusses an effective permutation-based approach to solve order-constrained testing problems, which are very difficult or even impossible to solve within the framework of parametric likelihood. The nonparametric combination (NPC) methodology is a flexible tool which relies on dependent permutation tests and allows us to deal with a large variety of complex testing problems, including the stochastic dominance and monotonic stochastic ordering problems of interest. To deal with them in line with Roy’s Union-Intersection (UI) approach, the NPC procedure decomposes the original hypothesis into suitable sub-hypotheses. In this article we discuss and compare two possible types of decomposition, exploiting an extensive simulation study. A real data application is also proposed, in which multivariate ordinal data from the medical field are analyzed.

Optimal insurance contract design with government disaster relief

AbstractI examine the design of optimal insurance contracts considering the possibility of government disaster relief payments. This work focuses on the impact of (risky and ambiguous) government disaster relief on the shape of optimal private insurance contracts. I demonstrate that the optimal insurance contract is a straight deductible contract in the case of a fixed probability of government relief. This result is robust to ambiguity in the probability of relief payments, even for ambiguity‐averse decision makers. If government disaster relief becomes more likely for larger losses, then the optimal insurance contract features coinsurance above a deductible. I also extend this analysis to more general stochastic dominance relationships between disaster relief and loss magnitude.

An econometric identification of ineffective common-cold advertising

PurposeThis study aims to highlight potential savings in advertising budgets.Design/methodology/approachThis study uses modern computer-based tools including stochastic dominance to check if advertising expenses are increasing sales by using modern causality assessment tools which allow for nonlinearities and use sophisticated assessment of causal impact of ads on sales.FindingsThis study identifies specific media spots where ad budget savings are possible. The marketing managers can take the next step to make small-scale local experiments to reassess this study’s findings.Research limitations/implicationsThis study is a statistical observational assessment not based on controlled experiments.Practical implicationsThe authors have tools to identify ineffective advertising which can produce huge savings for the organization. The over-the-counter cold remedies have become important due to the pandemic. The tools have wider applicability in marketing research.Social implicationsLess wasteful expenses always benefit the society.Originality/valueTo the best of the authors’ knowledge, this may be the first such attempt to use sophisticated causal identification tools. Remedies for the common cold sold by seven major US retailers help identify specific retailers and specific media with negative returns on investment.

An Intelligent Bat Algorithm for Web Service Selection with QoS Uncertainty

Currently, the selection of web services with an uncertain quality of service (QoS) is gaining much attention in the service-oriented computing paradigm (SOC). In fact, searching for a service composition that fulfills a complex user’s request is known to be NP-complete. The search time is mainly dependent on the number of requested tasks, the size of the available services, and the size of the QoS realizations (i.e., sample size). To handle this problem, we propose a two-stage approach that reduces the search space using heuristics for ranking the task services and a bat algorithm metaheuristic for selecting the final near-optimal compositions. The fitness used by the metaheuristic aims to fulfil all the global constraints of the user. The experimental study showed that the ranking heuristics, termed “fuzzy Pareto dominance” and “Zero-order stochastic dominance”, are highly effective compared to the other heuristics and most of the existing state-of-the-art methods.

Complete convergence and complete moment convergence for maximal weighted sums of arrays of rowwise extended negatively dependent random variables with statistical applications

In this paper, complete convergence and complete moment convergence for maximal weighted sums of arrays of rowwise extended negatively dependent random variables are investigated, and some sufficient conditions for convergence are provided. Three ways of optimising the conditions for convergence, namely reducing the moment condition, narrowing the boundary function, and raising the weight function respectively, are considered under light weights. Besides, rather than assuming stochastic domination, we turn to a weaker assumption of uniformly bounded expectations to describe the moment conditions. The results obtained in the paper extend the corresponding ones for independent random variables and some dependent random variables. In addition, the results are applied to establish strong consistency for estimators in some statistical models.

Double-Exponential-X Family of Distributions: Properties and Applications

A new family of distribution named Double-Exponential-X family is proposed. The proposed family is generated from the double exponential distribution. The forms of the probability densities and hazard functions of two distinct subfamilies of the proposed family are examined and reported. Generalproperties such as moment, survival, order statistics, probability weighted moments and quartile functions of the models are investigated. A sub family of the developed family of double –Exponential-X family of the distribution known as double-Exponential-Pareto distribution was used to fit a real life data on the use of antiretroviral drugs. Molecular simulation of efficacy of antiretroviral drugs is conducted to evaluate the performance of the model. The models were tested using some models diagnostic tests and it was revealed that the proposed model was better than the ones proposed before it from the same family and also, stochastic dominance method was used to affirm the best antiretroviral drugs used in the study.

The role of environmental and financial motivations in the adoption of energy-saving technologies: Evidence from European Union data

This paper investigates whether households’ environmental and financial motivations affect their investments in energy-saving technologies. Exploiting a comprehensive dataset covering 30 European countries, we investigate whether financially motivated and environmentally minded households present different adoption paths. The results show that environmental and financial motivations play an essential role in the decision to adopt energy-saving technologies, thus paving the way for policy actions targeted at enhancing consumer awareness. Our analysis also reveals that environmentally and financially motivated households exhibit different socio-economic profiles. We find that environmentally minded, highly educated households living in urban areas with a large family size are more likely to adopt energy-saving technologies than their counterparts with low levels of education living in rural locations. In addition, their financial situation is an important factor in explaining the adoption patterns of financially motivated households. From a methodological point of view, our analysis exploits both parametric and nonparametric methods. We use stochastic dominance analysis to rank the distribution functions of household behaviours and the logit model to investigate the socio-economic profiles of different groups.

Multiobjective portfolio optimization: Forecasting and evaluation under investment horizon heterogeneity

AbstractThis study designs a methodological framework to forecasting allocation weights and evaluating multiobjective portfolios considering the investment horizon heterogeneity. The investment horizon heterogeneity may induce the terrible data loss problem under traditional asset return definition, while in the real world, there are many portfolio makers whose investment horizons are not consistent. The methodological framework has three parts. First, this paper gives a novel multitimescale analysis (MTA) tool as a computation procedure to decompose the raw return series, and the decomposed subreturn series could represent the information for a portfolio maker with specific investment horizon and has the same data length as the raw return series. Second, proposed methodological framework uses a time‐varying parameter GAS‐D‐Vine‐Copula model to construct the joint distribution of subreturn series of multiassets in a portfolio. Third, due to the stochastic dominance consistency issue, this paper applies three different utility functions as the outputs of a portfolio strategy and two cost functions as the inputs of a portfolio strategy in an efficiency evaluation model. The empirical example of US aviation stock market data from 2013 to 2021 reveals that the Mean‐Skewness‐Volatility‐HMCR‐LPM multiobjective has the greatest numbers of optimal strategy timings for portfolio makers with 2‐, 3–5‐, and 10–50‐day‐length investment horizons. The investment horizon of 1‐day length is the least efficient, and the investment horizon between 10‐ and 50‐day length is the most efficient. The proposed methodology indicates that more multiobjectives in a portfolio strategy are not necessarily better, and there is an optimal range of investment horizons for portfolio makers.

Optimizing Erlangization-based approximations for finite discrete distributions and discrete phase-type distributions

In He et al.[8], continuous phase-type (PH) distributions are constructed to approximate finite discrete probability distributions and discrete PH-distributions. The approximations are based on Erlangization with a fixed number of phases. In this article, we first introduce continuous PH approximations with Erlang distributions of different orders. Then we develop an algorithm to find the continuous PH approximation with the minimum variance, among all such PH approximations with the same total number of phases. Thus, the proposed continuous PH approximations lead to a smaller gap between the variances of the Erlangization-based approximations and the original discrete random variables, which is achieved without adding more phases. The new approximations are useful to mitigate the burden in computation caused by the large number of phases needed in Erlangization approximation. Stochastic dominance is shown between the original (discrete) distributions and the approximations, which leads to bounds on the quantities of original distributions and/or stochastic models (e.g., reliability models). The approximation method is applied to analyze reliability models and a COVID-19 isolation program.

Customer satisfaction evaluation for drugs: A research based on online reviews and PROMETHEE-Ⅱ method.

Online reviews of consumers after purchasing drugs online reflect the factors affecting their satisfaction. How to understand customer satisfaction through online reviews and tapping their needs to improve satisfaction has become an urgent issue facing pharmaceutical e-commerce companies. Based on the online reviews of Alibaba Health Pharmacy, six representative OTC online medicines were selected for this study, including the following categories: tonics, anti-cold drugs, rheumatism and orthopaedic drugs, skin drugs, gastrointestinal drugs, vitamins, and calcium. By training and testing the LDA topic model, five potential topics are extracted as factors affecting customer satisfaction, including drug efficacy, drug cost performance, online customer service, logistics and transportation, and packaging. In this paper, Sentiment Analysis is used to process the review text to quantify the sentiment tendency of the review, and determine the evaluation scale value. Then, the random dominance among various drug factors is determined based on the Stochastic Dominance Rules. Finally, the PROMETHEE-Ⅱ method is used to determine the ranking value of the importance of each factor. The results suggest that the factors in different types of OTC drugs rank differently, which is also rationalized in this paper. This study provides a significant reference for improving customer satisfaction with pharmaceutical e-commerce.