Sampling studies on a test against trend in binomial data

Summary A series of 375 “Monte-Carlo” realizations were performed on a number of groupings of 100 samples each fromt distinct binomial populations (t=3, 4, 5, 7, 9) in order to obtain estimates of the power function of theV andX ² index of dispersion tests in detection of a “trend” in the binomial probabilities.     

Social Distance,Respondent Cooperation and Item Nonresponse in Sex Survey

This paper examines the ways in which the number of item nonresponses is determined by social distance and/or interview rapport, with a focus on responses of “refusal” and “don’t know”, implying the respondent’s lack of willingness and ability to provide substantive responses to sensitive questions. The data analyzed were from 39 self- administered questions concerning sexual attitudes and behaviors in the 2002 Taiwan Social Change Survey for module “Family and Changing Gender Role”. Poisson Regression in 2-level Hierarchical Linear Model was employed to enhance the accuracy of the analysis of the accumulation of “don’t know” and “refusal” responses. The results showed that respondent cooperation significantly decreased the number of both “don’t know” and “refusal” replies. The decrease was not conditioned by any kind of social distance. Age and education distances have respectively negative and positive effect on the number of “don’t know” and “refusal” answers. The married–married interview produced more “don’t know” and “refusal” than other paired interview types. The larger the ethnicity distance is, the more “refusal” appears. The substantial findings imply that the effects of social-distance and rapport (respondent cooperation) on the number of item nonresponses deserve more attention in research on survey methodology. The divergent findings on gender-distance effect and marital-status effect, however, call for replication studies in the future.     

Consistent estimation in the bilinear multivariate errors-in-variables model

A bilinear multivariate errors-in-variables model is considered. It corresponds to an overdetermined set of linear equations AXB=C, A∈ℝ^m×n, B∈ℝ^p×q, in which the data A, B, C are perturbed by errors. The total least squares estimator is inconsistent in this case.  An adjusted least squares estimator is constructed, which converges to the true value X, as m →∞, q →∞. A small sample modification of the estimator is presented, which is more stable for small m and q and is asymptotically equivalent to the adjusted least squares estimator. The theoretical results are confirmed by a simulation study. Acknowledgements. We thank two anonymous reviewers for their suggestions and corrections.? A. Kukush is supported by a postdoctoral research fellowship of the Belgian office for Scientific, Technical and Cultural Affairs, promoting Scientific and Technical Collaboration with Central and Eastern Europe.? S. Van Huffel is a full professor with the Katholieke Universiteit Leuven.? I. Markovsky is a research assistant with the Katholieke Universiteit Leuven.? This paper presents research results of the Belgian Programme on Interuniversity Poles of Attraction (IUAP V-22), initiated by the Belgian State, Prime Minister's Office – Federal Office for Scientific, Technical and Cultural Affairs of the Concerted Research Action (GOA) projects of the Flemish Government MEFISTO-666 (Mathematical Engineering for Information and Communication Systems Technology), of the IDO/99/03 project (K.U. Leuven) “Predictive computer models for medical classification problems using patient data and expert knowledge”, of the FWO projects G.0078.01, G.0200.00, and G0.0270.02.? The scientific responsibility is assumed by its authors.     

Verbesserung des nicht-randomisierten exakten Testes von R.A. Fisher

Summary The so-called Exact Test of R. A. Fisher for comparing two probabilitiesp ₁ andp ₂ in a Fourfold-Table with small cell frequencies is known as a UMPU-Test. But in practice the test is used in a nonrandomized, often tabulated version. Given a certain level of significanceα it is shown: the critical region of this nonrandomized test, referred to as “Fisher 1”, can be enlarged considerably. For instance for all sample-size-sums up to 20 andα=0.01 the total number of points in the critical regions of “Fisher 1” is 552 whereas the analogous number of the new version “Fisher 2” is 788. The size of tables for “Fisher 2” can be reduced considerably because the main parts of the critical regions can be described by the aid of some Chi-square-test versions. In particular Yates’ continuity-correction turns out to be always conservative in the above mentioned region relative to “Fisher 2” whereas this is not strictly true relative to “Fisher 1”.      

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.

     

Some models and measures for evaluating performances with DEA: past accomplishments and future prospects

This paper covers some of the past accomplishments of DEA (Data Envelopment Analysis) and some of its future prospects. It starts with the “engineering-science” definitions of efficiency and uses the duality theory of linear programming to show how, in DEA, they can be related to the Pareto–Koopmans definitions used in “welfare economics” as well as in the economic theory of production. Some of the models that have now been developed for implementing these concepts are then described and properties of these models and the associated measures of efficiency are examined for weaknesses and strengths along with measures of distance that may be used to determine their optimal values. Relations between the models are also demonstrated en route to delineating paths for future developments. These include extensions to different objectives such as “satisfactory” versus “full” (or “strong”) efficiency. They also include extensions from “efficiency” to “effectiveness” evaluations of performances as well as extensions to evaluate social-economic performances of countries and other entities where “inputs” and “outputs” give way to other categories in which increases and decreases are located in the numerator or denominator of the ratio (=engineering-science) definition of efficiency in a manner analogous to the way output (in the numerator) and input (in the denominator) are usually positioned in the fractional programming form of DEA. Beginnings in each of these extensions are noted and the role of applications in bringing further possibilities to the fore is highlighted.

The Dirty Dozen: Common Problem Areas in Principal–Agent Relationships

The main purpose of the article is to educate managers about potential difficulties caused by breach of fiduciary duties on the part of agents/employees within their organization. Managers will learn how to recognize common problem situations so they can take steps to avoid, or at least mitigate, any resulting damage. This article highlights 12 frequent situations—the “dirty dozen”—that pose dangers for business organizations.     

Determining of threat perceptions affecting direction of the US defense expenditures by using ordinal regression models

The article examines whether the US threat perceptions defined in terms of federal government national defense outlays in billions of constant (FY 2000) dollars change along with periodical changes in international politics between 1945 and 2007. Three different models affecting direction of the US defense expenditures are developed. The first model are estimated by using five link functions even though results of only two of them, complementary log–log and cauchit, are presented. As complementary log–log produced the best results, others models are predicted by using only this function. The parameter estimates of complementary log–log function for the first model indicate that four of these variables (Ford, Carter, Reagan and Bush Sr.) out of eleven are significant in the category of presidents. “Truman Docrtrine/Cominform”, “Korean War”, “Vietnam War”, and “Invasion of Iraq” also seem to be the important independent variables on empirical grounds for the first model. While “Party”, “Invasion of Iraq”, “Vietnam War”, “Korean War”, and “Cuban Missile Crisis” constitute the important independent variables on empirical grounds for the second model, “Korean War”, “Vietnam War”, “Invasion of Iraq”, “Truman Docrtrine/Cominform”, “The Cold War and New World Order”, and “Cuban Missile Crisis” are important independent variables on empirical grounds for the third model. Estimations based on these three models therefore suggest that aforementioned independent variables do indeed have effect on the US defense expenditures.     

Nonparametric regression function estimation using interaction least squares splines and comlexity regularization

Let (X, Y) be a pair of random variables withsupp(X)⊆[0,1] ^l andEY ²<∞. Letm ^* be the best approximation of the regression function of (X, Y) by sums of functions of at mostd variables (1≤d≤l). Estimation ofm ^* from i.i.d. data is considered. For the estimation interaction least squares splines, which are defined as sums of polynomial tensor product splines of at mostd variables, are used. The knot sequences of the tensor product splines are chosen equidistant. Complexity regularization is used to choose the number of the knots and the degree of the splines automatically using only the given data. Without any additional condition on the distribution of (X, Y) the weak and strongL ₂-consistency of the estimate is shown. Furthermore, for everyp≥1 and every distribution of (X, Y) withsupp(X)⊆[0,1] ^l ,y bounded andm ^* p-smooth, the integrated squared error of the estimate achieves up to a logarithmic factor the (optimal) rate      

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 identification of the significant independent variables in linear models

Summary Methods for the identification of the significant independent variables in multiple linear regression and in the multiple regression approach to non-orthogonal analysis of variance and covariance are discussed. “Forward Ranking” and “Backward Ranking” (by order of importance) of the independent variables are defined, and the backward method is shown to avoid the disadvantageous effects of “Compounds” upon the ranking. For non-orthogonal analysis of variance, a unique orthogonal decomposition of the regression sum of squares (due to all ANOVA effects) is shown to be possible when the groups of independent variables (representing the effects) are ranked by the criterion of “Non-Significance” and under “Restricted Admissibility.” A computer program is outlined which incorporates the proposed methods.

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Zusammenfassung Methoden für die Identifizierung der signifikanten unabh?ngigen Ver?nderlichen in der mehrfachen linearen Regressionsrechnung und im Regressionsverfahren für nichtorthogonale Varianz- und Kovarianzanalyse werden besprochen. „Vorw?rtsgerichtetes“ und „rückw?rtsgerichtetes“ Rangordnen (nach Bedeutung) der unabh?ngigen Ver?nderlichen werden definiert, und es wird gezeigt, da? beim rückw?rtsgerichteten Rangordnen die nachteiligen Wirkungen von „Verb?nden“ auf das Ordnen vermieden werden. Für den Fall der nichtorthogonalen Varianzanalyse wird gezeigt, da? eine eindeutige orthogonale Zerlegung der Quadratsumme für die Regression (erkl?rt durch die Gesamtheit der Haupt- und Wechselwirkungen in der Varianzanalyse) erreicht werden kann, wenn die Gruppen der unabh?ngigen Ver?nderlichen, die die Haupt- und Wechselwirkungen repr?sentieren, nach dem Rangordnungskriterium „Nicht-Signifikanz“ und unter „Beschr?nkter Zul?ssigkeit“ geordnet werden. Ein Rechenprogramm wird erl?utert, welches auf den vorgeschlagenen Methoden basiert.

     

A general class of estimators for estimating population mean using auxiliary information

Summary A general class of estimators for estimating the population mean of the character under study which make use of auxiliary information is proposed. Under simple random sampling without replacement (SRSWOR), the expressions of Bias and Mean Square Error (MSE), up to the first and the second degrees of approximation are derived. General conditions, up to the first order approximation, are also obtained under which any member of this class performs more efficiently than the mean per unit estimator, the ratio estimator and the product estimator. The class of estimators in its optimum case, under the first degree approximation, is discussed. It is shown that it is not possible to obtain optimum values of parameters “a”, “b” and “p”, that are independent of each other. However, the optimum relation among them is given by (b−a)p=ρ C _y/C _x. Under this condition, the expression of MSE of the class is that of the linear regression estimator.     

A new interpretation of optimality forE-optimal designs in linear regression models

The optimal design problem for the estimation of several linear combinationsc′ _l ϑ (l=1, …,m) is considered in the usual linear regression modely=f′(x)ϑ (f(x) ∈ ℝ ^k ,ϑ ∈ ℝ ^k ). An optimal design minimizes a (weighted)p-norm of the variances of the least squares estimates for the different linear combinationsc′ _l ϑ. A generalized Elfving theorem is used to derive the relation of the new optimality criterion to theE-optimal design problem. It is shown that theE-optimal design for the parameterϑ minimizes such a (weighted)p-norm whenever the vectorc=(c′ ₁, …, c′_k)′ is an inball vector of a symmetric convex and compact “Elfving set” in.     

Tests for departure from normality in the case of linear stochastic processes

Summary In this paper the asymptotic distributions of the third and the fourth sampling moments of a discrete-parameter linear process are derived together with the asymptotic distributions of the sampling skewness and the excess of kurtosis. The knowledge of these distributions allows us, in the case of “large” samples, to test the departure from normality, a problem which can be regarded as important in various practical applications, but which cannot be treated with the aid of classical tests based on the assumption that the sample values are independent. Some numerical examples illustrate the applications of the proposed tests in practice.

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Zusammenfassung In diesem Beitrage sind die asymptotischen Stichprobenverteilungen der dritten und vierten Momente eines linearen stochastischen Prozesses und auch die asymptotischen Stichprobenverteilungen der Schiefe und des Exzesses der Kurtosis hergeleitet. Die Kenntnis dieser Verteilungen erlaubt für “gro?e” Stichproben die Abweichung der Proze?verteilung von der Normalverteilung zu prüfen, ein Problem, das in vielen F?llen der praktischen Anwendungen wichtig ist, aber mit den klassischen Testen, welche die Unabh?ngigkeit der Stichprobenwerte annehmen, nicht behandelt werden kann. Die praktische Anwendung der vorgelegten Methode ist mit einigen numerischen Beispielen illustriert.

     

The Use of Mixed Methods Models and Designs in the Human Sciences: Problems and Prospects

The article explores some of the emerging issues in the newly developing area of Mixed Methods (MM) research. Two of these issues concern the possibility of whether MM can provide for both “diverse” and “severe” testing. Based on a model of Placeholder Effects and utilizing an example of current empirical research, it is concluded that certain varieties of MM are potentially more robust than others in fulfilling the diverse and severe criteria. It is also argued that MM must concern itself with formulating “procedural rules” which guide the researcher in choosing and applying appropriate strategies for specific research problems.     

One-Step and Two-Step Estimation of the Effects of Exogenous Variables on Technical Efficiency Levels

Consider a stochastic frontier model with one-sided inefficiency u, and suppose that the scale of u depends on some variables (firm characteristics) z. A one-step model specifies both the stochastic frontier and the way in which u depends on z, and can be estimated in a single step, for example by maximum likelihood. This is in contrast to a two-step procedure, where the first step is to estimate a standard stochastic frontier model, and the second step is to estimate the relationship between (estimated) u and z.In this paper we propose a class of one-step models based on the scaling property that u equals a function of z times a one-sided error u ^* whose distribution does not depend on z. We explain theoretically why two-step procedures are biased, and we present Monte Carlo evidence showing that the bias can be very severe. This evidence argues strongly for one-step models whenever one is interested in the effects of firm characteristics on efficiency levels.     

A generalized maximum likelihood characterization of the normal distribution

LetP be a probability measure on ℝ andI _x be the set of alln-dimensional rectangles containingx. If for allx ∈ ℝⁿ and θ ∈ ℝ the inequality holds,P is a normal distributioin with mean 0 or the unit mass at 0. The result generalizes Teicher’s (1961) maximum likelihood characterization of the normal density to a characterization ofN(0, σ²) amongall distributions (including those without density). The m.l. principle used is that of Scholz (1980).     

The equal pay act: Responsibilities and rights

The Equal Pay Act of 1963 (EPA) requires that men and women receive equal pay for equal work. Plaintiffs who claim discrimination on the basis of the EPA may settle out of court, or may bring legal action in the courts. Employers possess specific rights under the law, and can defend themselves against charges of discrimination through a number of “employer defenses.” These defenses involve providing that pay differences are based on seniority systems, merit systems, production systems, or “any other factor other than sex.” This article will also discuss the impact of court decisions that have further honed the responsibilities and rights of both employees and employers under the EPA.     

Musgrave’s vision of the public sector: the complex relationship between individual, society and state in public good theory

Richard Musgrave introduced the notion of a public good after reading an obscure publication by Lindahl in German in 1910. His great contribution to knowledge was to provide a clear and comprehensive structure for thinking about the process of achieving an “optimal” allocation of resources across public and private goods based individual preferences and the role of government in that process. A number of ambiguities and issues in Musgrave’s vision remain only partially resolved including the need to incorporate “higher laws” or community values into the allocation process.      

Queueing with reneging

Summary In this paper we consider a queue in which a person, having joined, may decide to leave and give up service if it appears that the time consumed will exceed some maximum which he has available. Specifically, three problems are treated: a) How to make a rational (sequential) decision while waiting in the queue, b) the probable effect of this decision, and c) the behavior of a queue in which all persons are employing such a procedure.

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Zusammenfassung Dieser Bericht behandelt eine “Schlange”, in der ein sich dieser “Schlange” angeschlossener Mensch entschlie?t, seinen Platz und die Bedienung aufzugeben wenn es ihm scheint, da? die notwendige Zeit ein ihm zur Verfügung stehendes Maximum überschreiten wird. Insbesondere werden drei Probleme diskutiert: a) Wie man eine rationale (sequentielle) Entscheidung trifft, w?hrend man in einer “Schlange” wartet, b) der wahrscheinliche Effekt einer solchen Entscheidung, c) das Benehmen einer “Schlange”, in dem alle Menschen ein solches Verfahren gebrauchen würden.