On the active approach of stochastic linear programming

Summary The problem of statistical distribution of the optimal objective function under the so-called active approach of stochastic linear programming is investigated here from two interrelated aspects. First, the active approach is viewed as a method of decomposition. Second, some results on the asymptotic form of distribution of extreme values are utilized to derive the asymptotic form of the distribution of the maximand under the active approach. Research done under the partial support of the U.S. National Science Foundation Grant No. 420-04-62 at the Department of Economics, Iowa State University. Some of the work related to this paper may be found in the following references:Sengupta, J. K., G. Tintner, andC. Millham: “On Some Theorems of Stochastic Linear Programming”. Management Science, Vol. 10, October 1963, pp. 143–159.Sengupta, J. K.: “The stability of truncated solutions of stochastic linear programming”. Econometrica, Vol. 34, January 1966. pp. 77–104.Sengupta, J. K.: “On the stability of solution under recursive programming”. Metrika 1966.Sengupta, J. K. andT. Kumar: “An application of sensitivity analysis to a linear programming problem”. Unternehmensforschung, Vol. 9, 1965.     

Social networks and labour productivity in Europe: an empirical investigation

This paper uses firm-level data recorded in the Amadeus database to investigate the distribution of labour productivity in different European countries. We find that the upper tail of the empirical productivity distributions follows a decaying power-law, whose exponent α is obtained by a semi-parametric estimation technique recently developed by Clementi et al. [Physica A 370(1):49–53, 2006]. The emergence of “fat tails” in productivity distribution has already been detected in Di Matteo et al. [Eur Phys J B 47(3):459–466, 2005] and explained by means of a model of social network. Here we show that this model is tested on a broader sample of countries having different patterns of social network structure. These different social attitudes, measured using a social capital indicator, reflect in the power-law exponent estimates, verifying in this way the existence of linkages among firms’ productivity performance and social network.     

Social Structural Inquiries,Part 1, Qualitative and Quantitative Theories

A tightened linkage between theory and data would enhance cumulative sociological knowledge. Toward that end this article selectivity reviews and develops social structural theories – theories that explain data. To reestablish that qualitative as well as quantitative theories can be structural, it presents examples that are organized by the qualitative versus quantitative division and the level of analysis – micro, meso, macro, and the world. Boudon’s structural schematics cover all of the examples, suggesting a basic perspective that can refocus much of the diversity of current sociology.     

Streuungszerlegung für Paar-Vergleiche

Zusammenfassung Pl?ne für Paar-Vergleich Versuche werden gegeben und die Auswertung solcher Versuche wird beschrieben. Die Arbeit st?tzt sich auf das vonBock (1958) abge?nderte Modell vonThurstone undMosteller (1951a). Die Pl?ne sind so, da? sie zu unabh?ngig verteilten Fehlern führen. Zu ihrer Auswertung kann bedenkenlos die Streuungszerlegung angewendet werden. Die Konstruktion von ausgewogenen Pl?nen (allek(k−1)/2 m?glichen Paare werden verglichen) wird beschrieben und teilweise ausgewogene Pl?ne (nicht alle m?glichen Paare werden verglichen) für bis zu 10 Objekte sind tabelliert. Es wird gezeigt, da? die Auswertung solcher Versuche mit der Auswertung von Versuchen in unvollst?ndigen Bl?cken identisch ist. Zur leichteren Auswertung der teilweise ausgewogenen Versuche sind die Inversen der Koeffizientenmatrix der Normalgleichungen tabelliert. Ein Anwendungsbeispiel aus der Wollforschung wird durchgerechnet.

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Summary Designs for paired comparisons are given and their analysis is discussed. The paper is based onBock’s modification (1958) ofThurstone andMosteller’s (1951a) model. The designs lead to independently distributed errors and analysis of variance can be applied. The construction of balanced designs (in which allk(k−1)/2 possible comparisons are made) is described and partially balanced designs (in which not all possible comparisons are made) for up to 10 objects are tabulated. It is shown that the analysis of paired comparison experiments is identical to the analysis of incomplete block experiments. To simplify the analysis of the partially balanced designs the inverses of the matrices comprising the coefficients of the normal equations are tabulated. A worked example of application to a problem in wool research is given.

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Die Arbeit wurde im South African Wool Textile Research Institute, Rhodes University, Grahamstown, Südafrika, geschrieben.     

On a noncentral chi-square distribution in the analysis of weapon systems effectiveness

Summary A natural conjugate prior distribution for the parameters involved in the noncentral chi-square leads to many known distributions. The applications of the distributions thus obtained are briefly pointed out in evaluating the ‘kill’ probability in the analysis of weapon systems effectiveness. The ‘kill’ probabilities or the expected coverage are obtained associated with a gamma prior distribution and compared with those obtained byMcnolty. This paper is read in a symposium on Mathematical Sciences held under the auspices of Delhi University, Delhi im January 1966.     

Einige Bemerkungen zur statistischen Messung der Konzentration

Zusammenfassung Nach einer kritischen Analyse der Begriffe „absolute“ und „relative“ Konzentration werden einige Kriterien gegeben, die Ma?zahlen der absoluten oder der relativen Konzentration zu erfüllen haben. Hierauf wird untersucht, inwieweit die gebr?uchlichsten Ma?zahlen der Konzentration (Gini, Herfindahl, Münzner) diese Kriterien erfüllen. Dann wird gezeigt, da? sich eine vonAdam angegebene, sehr allgemeine Klasse von Ma?zahlen als Ma?zahlen der absoluten Konzentration qualifizieren; einige wichtige Spezialf?lle werden genauer untersucht. Im vorletzten Teil der Arbeit werden Ma?zahlen für die Ver?nderung der Konzentration diskutiert und schlie?lich an einem praktischen Beispiel erprobt.

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Summary After analysing the concepts of “absolute concentration” versus “relative concentration”, some criteria for coefficients of concentration are given to qualify them either as measures for absolute or for relative concentration. On the basis of these criteria, some well-known coefficients (Gini, Herfindahl, Münzner) are examined. Furthermore, it is shown that the measures of “predictivity” as given byAdam can be regarded as coefficients of absolute concentration; some important special cases (one of which the Herfindahl index) are investigated. Finally, measures for the change in concentration are developed and applied to a practical example.

     

Exploring Nonlinearities in Path Models

In causal analysis, path models are an appropriate tool for studying relationships between social phenomena. However, they assume linear linkages between variables, and hence they are not always suitable for describing the complexity and richness of relationships in social phenomena. The aim of this work is to propose an exploratory graphical method to evaluate if the phenomena under analysis are actually characterized by non-linear linkages. In particular, the method is well suited to discovering interactions between the observed variables in path models. The proposed approach, which does not depend on any hypothesis on the error distribution, is based on a series of plots that can be easily interpreted and drawn using standard statistical software. As an additional feature, the plots – which we call joint effect plots – support qualitative interpretation of the non-linear linkages after the path model has been specified. Finally, the proposed method is applied within a case study. Non-linearities are explored in a casual model aiming to find the determinants of remittances of a group of Tunisian migrants in Italy.     

The Quality of Data Obtained from Self-Completed Questionnaires in a Survey of High School Students

This study examines issues of data quality in a survey conducted in a nationwide probability sample of 8985 students in the last four years of high school education in Greece. Respondents completed an extensive questionnaire whose main topic of investigation was the use of licit and illicit substances (tobacco, alcohol, cannabis, etc.). We examined the effect of sex, age and school performance on data quality. Specifically, we related these factors to the probabilities of correctly observing filters in the questionnaire, of certain inconsistencies in responses, of reporting difficulty in understanding the questions and being able to answer honestly. It was found that all these factors have strong effects. Boys’ responses presented more problems than girls’ (median odds ratio in a series of separate logistic regressions = 1.35) and younger respondents’ more than older (median odds ratio 1.34 for ages 13–14 and 1.06 for ages 15–16, compared to ages 17–18). The strongest effect was related to school performance compared to the best students (school marks 18–20), median odds ratios were 1.31 for marks 15–17, 1.76 for 12–14 and 3.25 for 10–11. Implications for questionnaire design are discussed.     

Testing outliers from an exponential population

Summary Likes obtains the distributions ofDixon’s statistics for an exponential population and tabulates upper 100α% points (α=0.1, 0.05, 0.01) of some of these distributions. The distribution of these statistics can be expressed in terms of finite series of beta functions and hence the probabilities of the rejection of suspected observed outliers may be easily calculated on a desk calculator. Thus we may avoid the difficult task of tabulating 100α% values of these statistics.     

Social Structural Inquiries – Part 2: Statistical Methods and Process Models

A tightened linkage between theory and data would enhance cumulative sociological knowledge. Toward that end this article selectivity reviews and develops social structural theories – theories that explain data. It focuses on statistical methods and process models because both approaches advance cumulative social science, and the tension between their advocates works against disciplinary solidarity. Boudon’s structural schematics cover all of the examples, suggesting a common perspective that can lessen the friction among practitioners of these forms of quantitative analysis and refocus much of the diversity of current sociology. An erratum to this article is available at .     

Distribution of product statistics from aPareto population

Summary Distributions are derived of the product of sample values, the sample geometric mean, the product of two minimum values from sample of unequal size and product ofk minimum values from sample of equal size from aPareto population. The distributions can be conveniently transformed tox ². Paper presented at the Eastern Regional meeting of the Institute of Mathematical Statistics, Upton, Long Island, New York, April 27–29, 1966. Work done when the author was on the faculty of Western Reserve University, Cleveland, Ohio, U.S.A.     

On the positivity of a variance-estimator

Summary Murthy’s variance — estimator for the estimator obtained by him by unorderingDes Raj’s estimator is shown to be non-negative.     

Generalized entropies in coding theory

Equivalence of the generalized entropyH ^β (P, Φ _t ) defined in this paper andKapur’s entropy of orderα and typeβ, ie.H _α ^β (P), is established. The results given recently byCampbell follow as special cases. International Conference on System Sciences, Honolulu, January 1968.     

Further results on asymptotic normality I

Summary Starting fromLe Cam [1956], it was shown inMichel andPfanzagl [1970] that — under certain regularity conditions — a dominated family of probability measures withEuclidean parameter space behaves approximately like a family of normal distributions, if each probability measure is the independent product of a great number of identical components. It is the purpose of this paper to estimate the accuracy of such a normal approximation.     

A Q-Analysis of Census Data: Intra-Household Income Allocation and School Attendance in Chiapas, Mexico

Q-analysis, introduced by a mathematician Ron Atkin, is a useful tool to explore social structures. I introduce essential concepts and techniques of q-analysis to show q-analysis’s potential ability to analyze and extract information from census data – the work that most researchers have done mainly with statistical methods. Using Mexican census and q-analysis, I examine whether children of female-headed household aged 15–19 were more likely to attend school than male-headed household children in Chiapas, Mexico in 2000. My findings are consistent with the large body of previous research, many of which were conducted with statistical methods: women’s control of income tends to results in a better welfare for their children, defined as children’s school attendance by the sex of heads of household in my study. I evaluate the advantages and disadvantages of a-analysis of census data. I conclude that while it has some weaknesses, q-analysis is a complimentary method to statistical methods for analysis of census data that may overcome some limitations that statistical methods often face such as an incapability of handling a small sample.     

Einige neuere Entwicklungen in der Messung der industriellen Konzentration

Zusammenfassung In der Diskussion verschiedener Konzentrationsma?e zeigt die Informationsentropie in der Form des normierten Entropiema?esE optimale Eigenschaften. Gleich demC-Index und demRosenbluth-Index reagiert sie wettbewerbstheoretisch „richtig“, weist aber wegen ihrer axiomatischen Fundierung zus?tzlich die Disaggregations-Eigenschaft auf. Zur ersten Orientierung über Konzentrationstendenzen hat sich der Konzentrationskoeffizient trotz mancher Nachteile als nützlich erwiesen. Einige Ergebnisse werden am Beispiel der Automobilproduktion Kanadas und der BRD gezeigt.

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Summary Among the discussed measures of business concentration the standardized entropy-measureE reveals most favourable properties. Alike the indexes ofHirschman and ofRosenbluth it reacts ‘as expected’ in terms of the theory of industrial organization. In addition,E makes disaggregation feasible because of its axiomatic basis. For purposes of observing concentration at a first glance the method of concentration ratios proves to be a useful tool despite conceptual shortcomings. Some findings are shown for the Canadian and the West-German passenger-car industry.

     

About probability-like measures for entire theories

5. Summary It is discursively argued that a much closer rapport between the methodologies implicitly taught in Economic Theory and in Statistics is required and that the necessary interdisciplinary bridge can be provided, and clarification attained, through the study of logical measure functions of theKemeny-Carnap type. It is also argued that subjectivistic axiom systems of probability, while valuable in their own right and as bases for behavior theories, cannot by themselves render the study of logical measure functions superfluous. Elementary aspects of these functions are then explained, with somewhat more detailed references toKemeny’s measuresm ands and a proposed degree-of-theoretization measure, whose applicability to economics is negatively appraised. Finally,Carnap’s degree-of-confirmation functions are briefly dealt with, but throughout the paper the emphasis is on those properties of logical measure functions which donot primarily bear on statistical inference and estimation). “...I think, on the whole, one theory fits nearly everything. That is, if you admit one coincidence—and I think one coincidence is allowable. More than one, of course, is unlikely ...” Prof. Dr. E. M. Fels, 2126 CL, University of Pittsburgh, Pittsburgh 13, Penna., USA. The Murder at the Vicarage. New York: Dell, 1961, p. 197 (Dodd, Mead & Co., 1930).     

A new extension of bivariate FGM copulas

We propose a new family of copulas generalizing the Farlie–Gumbel–Morgenstern family and generated by two univariate functions. The main feature of this family is to permit the modeling of high positive dependence. In particular, it is established that the range of the Spearman’s Rho is [ − 3/4,1] and that the upper tail dependence coefficient can reach any value in [0,1]. Necessary and sufficient conditions are given on the generating functions in order to obtain various dependence properties. Some examples of parametric subfamilies are provided.     

Assessing legitimation in mixed research: a new framework

In this article, we have merged or intersected two typologies: Greene’s (Res Sch 13(1):93–98, 2006) four-domain typology for developing a methodological or research paradigm in the social and behavioral sciences and Onwuegbuzie and Johnson’s (Res Sch 13(1):48–63, 2006) nine-component typology for assessing mixed research legitimation. We argue that merging or interconnecting these typologies present a framework for assessing legitimation in mixed research. Specifically, we demonstrate how the nine types of legitimation map onto Greene’s (Res Sch 13(1):93–98, 2006) four methodological domains and illustrate how legitimation in mixed research, rather than being viewed as a procedure that occurs at a specific step of the mixed research process, is better conceptualized as a continuous iterative, interactive, and dynamic process. Additionally, in presenting this framework, we hope to reduce misperceptions that some researchers have voiced about mixed research.     

A further note on the asymptotic efficiency of friedman’s x r 2 -test

Summary For independently distributed error components, the asymptotic relative efficiency (A.R.E.) ofFriedman’sx _r ² -tests with respect to the classical analysis of variance test has been studied byElteren andNoether andSen [1967]. The present note extends these results to the case of correlated errors arising in some random-effects or mixed-effects models. Work supported by the U.S. Army Research Office, Durham, Grant DA-ARO-D-31-124-G 746.