A numerical representation of semiorders on a countable set

Let be a semiorder on a countable setX and letx⁰ y if and only if either there existsx withxxy or there existsx withxxy. Then ⁰ is a preference relation with transitive indifference, which can be represented by a utility functionf of the usual sort. It is well known that is represented by a pair of real-valued functionsu, v, in the sense thatxy if and only ifu(x)>v(y). We prove that there exists a pair of functionsu, v, representing , such thatu+v is the utility function which represents in the usual sense. Moreover it is easily seen that, for such a pair of functionsu, v, we havex⁰ y if and only if eitheru(x)>u(y) or (u(x)=u(y) andv(x)>v(y)).

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Sommario Consideriamo unsemiordine su un insiemeX numerabile e poniamox⁰ y se e solo se esistex tale chexxy, oppure esistex tale chexxy. In questo caso ⁰ è unordine debole, che può essere rappresentato da una funzione di utilitàf nel senso usuale. D'altra parte è rappresentato da una coppia di funzioniu, v, nel senso chexy se e solo seu(x)>v(y). In questo lavoro si prova che ammette una rappresentazioneu, v tale chex⁰ y se e solo seu(x)+v(x)>u(y)+v(y). Si dimostra altresì che, con riguardo ad una siffatta rappresentazioneu, v di , riescex⁰ y se e solo seu(x)>u(y) oppure (u(x)=u(y) ed anchev(x)>v(y)).

     

On UMV-EStimators in survey sampling

Summary The existence of uniformly minimal variance estimators in the class of all linear unbiased estimators of the population total is discussed. Some remarks are given on the concept of necessary bestness.

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Zusammenfassung Es wird die Existenz von Schätzungen mit gleichmäßig minimaler Varianz in der Klasse aller linearen erwartungstreuen Schätzungen des Populationstotales besprochen. Einige Bemerkungen werden zum Begriffi necessary bestness gemacht.

     

Optimality of block designs with variable block sizes and random block effects

We consider the simple block model with random block effects, the block effects having variance _b ² =²;, with ² the variance of the errors. It is assumed that the experimenter can vary the sizes of the blocks. The universal optimality of certain designs for all over all designs with the same number of blocks and the same number of observations is shown. It is of interest to note that if Balanced Incomplete Block Designs compete, then they perform equally well for =0 and for =, i.e. in the one way classification model and in the simple block model with fixed block effects, but they perform worse for every (0, ).The result is, however, theoretical in nature. It treats a situation which is not very likely to happen in practice. The interest lies in the fact that it provides a counterexample to a conjecture on optimality of designs in mixed models.     

Two-dimensional Bernstein polynomial density estimators

A Bernstein polynomial estimator for f_nN(x, y) for an unknown probability density functionf(x, y) concentrated on the triangle ={(x, y): 0x, y<1,x+y<1} or on the square =(x, y):0 x, y 1 is developed. As a measure of quality the exact order of magnitude for the pointwise mean squared error is established. It is seen that the quality of these Bernstein polynomial estimators is comparable with the quality of the so-called kernel estimators. Further for such estimators uniform weak consistency results and central limit theorems are developed.     

Employee-initiated defamation lawsuits: Organizational responses and dilemmas

The fast-growing category of defamation lawsuits in the United States involves actions by employees against their employers. Over the last decade, the courts have increasingly ruled in favor of the employee plaintiffs, thus creating an employee's right to reputation. This article identifies a variety of responses undertaken by organizations to reduce their legal liability and lessen the likelihood of employee defamation lawsuits. We argue that while organizational actions to reduce their legal liability may appear rational, such responses may also be creating situations in which employers, employees, and the public may be the unintended victims of a law without justice. The article concludes with a discussion of balancing the freedom necessary for managers to communicate about employees and the fairness of that communication.     

On the reliability of the chi-square test

Summary The classical ₂ test of goodness of fit depends on the partition chosen to calculate it. In this work the covariance structure of the family of all ₂ tests obtained by translation (modulo 1) of a uniform partition of the interval [0, 1) it is determined, under the hypothesis of uniform distribution on [0, 1). This is used to define and compute an index which measure the indeterminacy of the ₂ test due to the arbitrary choice of the partition to compute it.     

Eine Invarianzeigenschaft für Startverteilungen einer Klasse stochastischer Prozesse

Summary This paper discusses some concepts of mixing for stochastic processes with discrete time. The idea of mixing, which is defined with respect to a starting distribution , means that the tranjectories of the process get out of any set with -measure zero with probability one. Such -mixing processes satisfy an invariance property; an asymptotic event has probability zero under any starting distribution, provided that it has probability zero under the starting distribution . Concerring stationary Markov chains these results imply a weak zero-one-law the relation of which with well-known stronger versions especially for aperiodic Harris chains and with the notions of weak ergodicity and a.s. triviality is studied.     

Eine simultane Charakterisierung der geometrischen Verteilung und der logistischen Verteilung

Summary LetE denote the generating function of a non-degenerate probability distribution on the positive integers, letF be a non-degenerate distribution function, and let be a real valued function on the interval (0, 1]. In the present paper the solutions (E, F, ) of the functional equationE(F(x)/E()=F(x+()), –<x<+, (0, 1] are given. It is shown that ifF is symmetric about zero,E andF belong to a solution of the functional equation if and only ifF is a logistic distribution andE is the generating function of a geometric distribution.     

The Irish Economic Resurgence and Small Nation Development

The success of the economy of the Republic of Ireland since the mid-1990s has prompted the characterization The Celtic Tiger. This paper describes the elements of the success and examines the strategic basis for it. Ireland's development strategy focused on building a consensus on fiscal and economic policy; capitalizing on membership in the European Union; promoting direct foreign investments with aggressive incentives; and cultivating a young and educated work force. Far from being a miracle, Ireland's success provides a model for economic development for small nations in a global economy. The authors examine and assess economic development efforts in Puerto Rico and Costa Rica in light of lessons learned from Ireland's experience.     

Minimal sufficient statistics for the group divisible partially balanced incomplete block design (GD-PBIBD) with interaction under an Eisenhart Model II

Summary In this paper, an Eisenmhart Model II with interaction for a GD-PBIB design withp replicates per cell is considered. Specifically the Model Y_ijl=µ+_i+_j+()_ij+e_ijl is assumed, wherei=1, 2, ...,b; j=1, 2, ...,t andl=0, 1, 2, ...p s _ij wheres _ij=1, if treatmentj appears in blocki, 0, otherwise.If _i, _j, ()_ij ande _ijl are normally and independently distributed, then a minimal sufficient (Vector-valued) statistic for the class of densities for this model is found, together with the distribution of each component in the minimal sufficient statistic. It is also shown that the minimal sufficient statistic for this class densities is not complete. Hence the solution of the problem of finding minimum variance unbiased estimators of the variance components is not straightforward.     

Das maximale signifikanzniveau des Tests: “LehneH o ab,wennk untern gegebenen tests zur ablehnung führen”

Summary On one sample space there aren tests with critical regionsK ₁ and levels of significance _i ,i=1, ...,n (resp.n eventsK _i in a probability space with probabilities not greater than _i ,i=1, ...,n). In this paper we calculate the smallest upper bound of the level of significance of the test reject the hypothesis, if at leastk among the,n tests do so (resp. of the probability of the event at leastk among then events are realized). By the way, we will show, that this smallest upper bound does not change, if we replace at leastk by exactlyk.     

Vergleich des verallgemeinerten nichtzentralent-Tests mit dem Binomialtest

Zusammenfassung Es sei {F _,(x); –<<, >0} mitF _,(x)=F((x–)/)–F(x) eine standardisierte Verteilungsfunktion — die Familie der zulässigen Verteilungsfunktionen. Der (früher eingeführte) verallgemeinerte nichtzentralet-Test für die Hypothese {PP ₀} mitP:=F _,(x ₀) gegen die Alternative {P>P ₀} zum Niveau wird mit dem entsprechenden nichtparametrischen Test (Test für die Hypothese {pP ₀} über den Parameterp einer Binomialverteilung gegen die Alternative {p>P ₀}) verglichen. Für dent-Test wird die relative asymptotische Effizienz bestimmt.Beide Tests lassen sich als Tests für das zur WahrscheinlichkeitP ₀ gehörende Quantil einer Verteilungsfunktion interpretieren. Der klassische zentrale Student-Test ergibt sich als Spezialfall (F(x)=(x),P ₀=0,5).

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Summary Let {F _,(x);–<<, >0} withF _,(x ₀):=F((x–)/–F(x) a standarized distribution function — the family of admissible distribution functions. The (earlier introduced) generalized noncentralt-test for the hypothesis {PP ₀} withP:=F _,(x ₀) against the alternative {P>P ₀} at level of significance is compared with the corresponding nonparametric test (Binomial test). The relative asymptotic efficiency of thet-test is determined. Both kinds of tests can be interpreted as quantiltests. In caseF(x)=(x),P ₀=0,5 one gets the classical central Student-test.

     

Effective participative decision making: A joint responsibility for success

Much of the current research on participative decision making focuses on the increasing need for broad-based decision-making systems, on the different outcomes associated with different forms of participation, or on the problems associated with poorly managed participative decision-making systems. This article considers the responsibilities of employees who participate in organizational decision making and the responsibilities of employers who expect to share decision-making tasks. A Bill of Responsibilities for Employees and a Bill of Responsibilities for Employers are presented. Pitfalls associated with neglecting these responsibilities are discussed.     

Relationship between generalizedh-Statistics and polykays

Summary In this paper, relationships between generalizedh-statistics which estimate powers and products of central moments unbiasedly and the polykays by using ordered partitions are established. A table expressing generalizedh-statistics of weight 12 in terms of polykays and vice versa is presented. Expressions of weight less than 12 are obtained from this table.

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Zusammenfassung In der vorliegenden Arbeit wird mittels geordneter Zerlegungen eine Beziehung zwischen verallgemeinerterh-Statistik, welche Potenzen und Produkte von zentralen Momenten erwartungstreu abschätzt, und polykays hergestellt. Eime Tabele mit verallgemeinerterh-Statistik vom Gewicht 12 in polykay-Termen, und umgekehrt, wird gegeben. Gewichtsausdrücke kleiner als 12 werden aus dieser Tabelle gewonnen.

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This research has been supported by a grant from FINEP/Ministério do Planejamento e Coordenacão Geral to the IMUFRJ.     

Law without justice: The dilemmas of formalization and fairness in the legalistic organization

There is growing evidence of a litigation mentality rampant in organizations, which has created a legalistic mindset in many managers. Increasingly, managerial decisions are becoming dominated by a concern for what is legally defensible at the expense of broader social considerations such as justice and fairness. The papers in this special issue explore how this legalistic mindset has created new organizational and social dilemmas, and situations of law whithout justice.     

Some brief notes on the “unfinished business” of qualitative inquiry

The paper argues that there are a variety of implicit issues in qualitative inquiry that need to be addressed if the area is to develop in some normal science sense. This unfinished business is concerned with a deeper investigation of basic terms that are now simply taken for granted, such as theme and pattern. It also includes the need to develop rules which will assist in making and justifying how qualitative interpretations are made from the implicit processes of inference. Specific suggestions are made for accomplishing these issues.     

The Effects of 9/11 and Terrorism on Human Resource Management: Recovery, Reconsideration, and Renewal

The United States suffered an unprecedented loss of life on September 11, 2001, from what was labeled a terrorist attack. Mainly on the basis of data from professional association surveys and government agencies, it was found that the United States and many other countries of the world have been significantly affected by the events and aftermath of that morning's events. As an unprecedented attack on a country not usually affected by external terrorism, it allows a unique study of how terrorism can affect countries in the world. As a result of 9/11 there were significant changes in the U.S. economy and society that, because of the global economy and politics as well as the international war on terrorism, certainly have international consequences. Changes also occurred in most areas of human resource management as well as producing a much greater emphasis on having an overall business crisis management program. However, many of the initial changes appear to have diminished over time. The resultant changes, and lack of changes, produce rich questions for further research.     

On estimating the variance of a finite population

Summary Observing that the estimator for a finite population variance as recommended byLiu [1974a, b] can sometimes become negative, we suggest a few non-negative alternative estimators and note some of their properties. UnlikeLiu we follow the conventional Bayesian approach to get another estimator with an optimal property of uniform admissibility.This paper, however, was prepared when the author worked in the Department of Economic Statistics, University of Sydney.     

State competition in higher education: A race to the top,or a race to the bottom?

How does competition affect higher education? This paper explores this question for public and private universities. Theory indicates that competition can push higher education policy in one of two different directions. On the one hand, competition may increase spending. For states, this would occur if states treat higher education as developmental; for private universities this would occur if they view spending as a means to attract students and prestige. On the other hand, competition may decrease spending if states treat higher education spending as redistributive, and competition may decrease spending by private schools if lower spending enhances their ability to attract students with low tuition. To determine which of these perspectives is most valid, we examine higher education policy choices in the 1980s and 1990s. We find that states appear to act as if higher education funding is redistributive while private schools appear to compete more on the basis of tuition than spending. These results demonstrate the important effects competition and governance structure have on higher education.Received: August 2001, Accepted: May 2002, JEL Classification: I2, I22, H72, I3     

Una classe di funzioni monotone generalizzate

Si considera la classe delle funzioni realiF(x,y) definite inS×S, conSR ^N , che soddisfano per ognix,yS la condizione di monotoniaF(x,y)+F(y,x)0. Indebolendo la precedente disuguaglianza si introducono classi di funzioni monotone generalizzate e, supponendo soddisfatta una opportuna condizione di omogeneità, si caratterizzano tali funzioni in base alla struttura del segno delle funzioni _{x, v} (t, s) = F(x + tv, x + sv), x S, v R ^N \{0}. Infine dopo aver definite le funzioni F-differenziabili, si introducono classi di funzioni conversse generalizzate, rispetto ad F, e si studiano i collegamenti tra queste classi e la monotonia generalizzata diF.

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Summary We consider the class of real valued functionF(x,y) defined inS×S, withSR ^N , satisfying x,yS the monotone conditionF(x,y)+F(y,x)0. Weakening the previous inequality we introduce the class of quasi-monotone, pseudo-monotone and strictly pseudo-monotone functions. Under a suitable assumption of homogeneity we characterize the generalized monotone functions studying the sign structure of the functions _{x, v} (t, s) = F(x + tv, x + sv), x S, v R ^N \{0}.Finally by means of the notion ofF-differentiability we introduce new classes of generalized convex functions (with respect toF) and we study the relationship between these classes and the generalized monotonicity ofF.

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Questa ricerca è stata parzialmente finanziata dal Ministero per l'Università e la Ricerca Scientifica.