Applications of random set theory in econometrics

In recent years, the econometrics literature has shown a growing interest in the study of partially identified models, in which the object of economic and statistical interest is a set rather than a point. The characterization of this set and the development of consistent estimators and inference procedures for it with desirable properties are the main goals of partial identification analysis. This review introduces the fundamental tools of the theory of random sets, which brings together elements of topology, convex geometry, and probability theory to develop a coherent mathematical framework to analyze random elements whose realizations are sets. It then elucidates how these tools have been fruitfully applied in econometrics to reach the goals of partial identification analysis.

Is output performance all about the resources? A fuzzy-set Qualitative Comparative Analysis of street-level bureaucrats in Switzerland

This article refines Lipsky’s (1980) assertion that lacking resources negatively affect output performance. It uses fuzzy-set Qualitative Comparative Analysis to analyse the nuanced interplay of contextual and individual determinants of the output performance of veterinary inspectors as street-level bureaucrats in Switzerland. Moving ‘beyond Lipsky’, the study builds on recent theoretical contributions and a systematic comparison across organizational contexts. Against a widespread assumption, output performance is not all about the resources. The impact of perceived available resources hinges on caseloads, which prove to be more decisive. These contextual factors interact with individual attitudes emerging from diverse public accountabilities. The results contextualize the often-emphasized importance of worker-client interaction. In a setting where clients cannot escape the interaction, street-level bureaucrats are not primarily held accountable by them. Studies of output performance should thus sensibly consider gaps between what is being demanded of and offered to street-level bureaucrats, and the latter’s multiple embeddedness.

FORA - A Fuzzy Set Based Framework for Online Reputation Management

The Social Web offers increasingly simple ways to publish and disseminate personal or opinionated information, which can rapidly exhibit a disastrous influence on the online reputation of organizations. Based on social Web data, this study describes the building of an ontology based on fuzzy sets. At the end of a recurring harvesting of folksonomies by Web agents, the aggregated tags are purified, linked, and transformed to a so-called fuzzy grassroots ontology by means of a fuzzy clustering algorithm. This self-updating ontology is used for online reputation analysis, a crucial task of reputation management, with the goal to follow the online conversation going on around an organization to discover and monitor its reputation. In addition, an application of the Fuzzy Online Reputation Analysis (FORA) framework, lesson learned, and potential extensions are discussed in this article.

A Parametric Test of Perfect Ranking in Balanced Ranked Set Sampling

Many techniques based on data which are drawn by Ranked Set Sampling (RSS) scheme assume that the ranking of observations is perfect. Therefore it is essential to develop some methods for testing this assumption. In this article, we propose a parametric location-scale free test for assessing the assumption of perfect ranking. The results of a simulation study in two special cases of normal and exponential distributions indicate that the proposed test performs well in comparison with its leading competitors.

Detection of RTX toxin genes in gram-negative bacteria with a set of specific probes

The family of RTX (RTX representing repeats in the structural toxin) toxins is composed of several protein toxins with a characteristic nonapeptide glycine-rich repeat motif. Most of its members were shown to have cytolytic activity. By comparing the genetic relationships of the RTX toxin genes we established a set of 10 gene probes to be used for screening as-yet-unknown RTX toxin genes in bacterial species. The probes include parts of apxIA, apxIIA, and apxIIIA from Actinobacillus pleuropneumoniae, cyaA from Bordetella pertusis, frpA from Neisseria meningitidis, prtC from Erwinia chrysanthemi, hlyA and elyA from Escherichia coli, aaltA from Actinobacillus actinomycetemcomitans and lktA from Pasteurella haemolytica. A panel of pathogenic and nonpathogenic gram-negative bacteria were investigated for the presence of RTX toxin genes. The probes detected all known genes for RTX toxins. Moreover, we found potential RTX toxin genes in several pathogenic bacterial species for which no such toxins are known yet. This indicates that RTX or RTX-like toxins are widely distributed among pathogenic gram-negative bacteria. The probes generated by PCR and the hybridization method were optimized to allow broad-range screening for RTX toxin genes in one step. This included the binding of unlabelled probes to a nylon filter and subsequent hybridization of the filter with labelled genomic DNA of the strain to be tested. The method constitutes a powerful tool for the assessment of the potential pathogenicity of poorly characterized strains intended to be used in biotechnological applications. Moreover, it is useful for the detection of already-known or new RTX toxin genes in bacteria of medical importance.

Fast parallel kriging-based stepwise uncertainty reduction with application to the identification of an excursion set

Stepwise uncertainty reduction (SUR) strategies aim at constructing a sequence of points for evaluating a function  f in such a way that the residual uncertainty about a quantity of interest progressively decreases to zero. Using such strategies in the framework of Gaussian process modeling has been shown to be efficient for estimating the volume of excursion of f above a fixed threshold. However, SUR strategies remain cumbersome to use in practice because of their high computational complexity, and the fact that they deliver a single point at each iteration. In this article we introduce several multipoint sampling criteria, allowing the selection of batches of points at which f can be evaluated in parallel. Such criteria are of particular interest when f is costly to evaluate and several CPUs are simultaneously available. We also manage to drastically reduce the computational cost of these strategies through the use of closed form formulas. We illustrate their performances in various numerical experiments, including a nuclear safety test case. Basic notions about kriging, auxiliary problems, complexity calculations, R code, and data are available online as supplementary materials.