Characterizations of distributions via linearity of regression of generalized order statistics

Let X (r, n, m, k), 1 r n, denote generalized order statistics based on an absolutely continuous distribution function F. We characterize all distribution functions F for which the following linearity of regression holds E(X(r+l,n,m,k) | X(r,n,m,k))=aX(r,n,m,k)+b.We show that only exponential, Pareto and power distributions satisfy this equation. Using this result one can obtain characterizations of exponential, Pareto and power distributions in terms of sequential order statistics, Pfeifers records and progressive type II censored order statistics. Received July 2001/Revised August 2002     

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)).

     

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.     

RAM: A Range Adjusted Measure of Inefficiency for Use with Additive Models,and Relations to Other Models and Measures in DEA

Generalized Efficiency Measures (GEMS) for use in DEA are developed and analyzed in a context of differing models where they might be employed. The additive model of DEA is accorded a central role and developed in association with a new measure of efficiency referred to as RAM (Range Adjusted Measure). The need for separately treating input oriented and output oriented approaches to efficient measurement is eliminated because additive models effect their evaluations by maximizing distance from the efficient frontier (in ₁, or weighted ₁, measure) and thereby simultaneously maximize outputs and minimize inputs. Contacts with other models and approaches are maintained with theorems and accompanying proofs to ensure the validity of the thus identified relations. New criteria are supplied, both managerial and mathematical, for evaluating proposed measures. The concept of approximating models is used to further extend these possibilities. The focus of the paper is on the physical aspects of performance involved in technical and mix inefficiencies. However, an Appendix shows how overall, allocative and technical inefficiencies may be incorporated in additive models.     

Sexual harassment in organizations

Sexual harassment is now recognized as a potential problem for most organizations. The purpose of this paper is to provide an introduction to the various aspects of sexual harassment as a problem: its definition (including both the economic injury and hostile environment types of harassment), its characteristics, and a discussion of how to deal with such problems in the workplace. Organizations are encouraged to act affirmatively by (1) establishing a policy prohibiting sexual harassment in the organization; (2) establishing and making employees aware of a grievance procedure for sexual harassment complaints; and (3) educating employees about the problem of sexual harassment through a combination of awareness and experiential training techniques.     

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.     

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.     

Estimation of a regression coefficient after two preliminary tests of significance

Summary The estimation of the regression coefficient of a population, defined byE (y)= +x, incorporating two preliminary tests of significance has been discussed. The experimenter has two random samples of different sizes from two such populations, as defined above, with regression coefficients ₁ and ₂ respectively, where ₂ may possibly be equal to ₁. Besides this, it is also conjectured that the common conditional variance ² of the two populations has a specified value ₀ ² . The two preliminary tests are used to resolve these two uncertainties.The author has rejoined Lucknow University, Lucknow India on Oct. 4, 1976 after availing leave for two years.     

Charakterisierung der zweiseitigen Exponentialverteilung

LetF () be a family of distribution functions with a translation parameter such thatF (0) has a densityf. It is well known that each sample median is a maximum likelihood estimate of , iff belongs to the classE of all bilateral exponential densities which are symmetric about 0. Here it is shown that, conversely,fE holds, either if there is an evenm such that for every sample of sizem each median is an MLE of , or if there is an infinite setM such that for every sample of any sizemM at least one median is an MLE of .     

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.     

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     

Alcune proprieta′ di monotonia generalizzata

Questo lavoro pone la monotonia generalizzata come un opportuno strumento per uno sviluppo controllato di funzioni scalari e vettoriali. E' cosi possibile caratterizzare la relazione tra su spazi vettoriali.

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Summary Some generalized monotonicity properties are analyzed both for scalar and vector functions. In particular the relation between and the class of functions, which are able to preserve it, are studied.

     

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.     

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.     

A dual approach for matrix-derivatives

Summary A dual approach for matrix by matrix derivatives is proposed, based on the work ofBalestra and the idea ofDwyer/MacPhail. The two derivative concepts are calledB-type derivative for the form B/A = (b _kl /A), because it was studied fully inBalestra, andA-type derivative for the form B/ /A = (B/a _ij ). Both derivative concepts are linked by permutation matrices, which also reveil the duality aspect more clearly, and can be transformed to each other very easily. The derivatives are applied to least squares estimates and posterior means in the general regression model and the seemingly unrelated regression (SUR)-system, introduced byZellner. The derivatives with respect to the covariance matrix is related to the local sensitivity concept ofLeamer [1978], while the derivatives with respect to the data-matrix, also called local resistance, is linked with the robustness concept ofTukey. The newly definedB-derivative enables an easier interpretation of the results.     

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.     

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.     

Informal pressures, mobilization, and campaigns in the management of centrally planned economies

Summary Following a short presentation of the striking deficiencies of plan instructions and financial regulation — the formal means of control of today's socialist centrally planned economies — we state that in actual fact these are not the basic means of control in these systems.The basic means of control is mobilization. Historically, this method originated from the declared unity of society. People — first of all economic managers — have to identify themselves with the objectives declared by the authorities. Moreover, the deficiencies of the formal means of control perpetuate the basic task assigned to mobilization.Campaigns are a specific kind of mobilization, meant for the implementation of new national economic objectives or tasks that have become newly important. Although mobilization facilitates the functioning of the economic system, we also have to underline two kinds of its negative consequences. First, mobilization oversimplifies the economic problems, tasks which in reality are tremedously complex. To be sure, some tasks can be implemented with its help, but certainly at high costs. Second, the never-ending repetition of the prevailing (campaign) slogans and the fact that they cannot be really contradicted weakens the capacity of central planners to forecast the future.This paper — the basic idea of which had already been present in Soós (1985) — was written while the author was visiting the European University Institute in April 1986, within the Research Project on East-West Trade and Financial Relations, directed by Professor D. M. Nuti. The paper was presented to the seminar of the working group on Comparative Economic Systems on 17 April 1986. The author wishes to thank Professor Paul Marer for his editorial help in preparing this final version.     

Realization of closed,convex, and symmetric subsets of the unit square as regions of risk for testing simple hypotheses

It is well-known that the region of risk for testing simple hypotheses is some closed, convex, and (1/2, 1/2)-symmetric subset of the unit square, which contains the points (0, 0) and (1, 1). It is shown that for any such subsetR of the unit square and any atomless probability measureP on some -algebra there exists some probability measureQ on the same -algebra such thatR is the corresponding region of risk for testingP againstQ. This generalizes a result of [4] and is as a first step derived here for the special case, whereP is equal to the uniform distribution on the unit interval. The corresponding distributionQ is given explicitly in this case and the general case is treated by some well-known measure-isomorphism. This method of proof shows thatQ might be chosen to be of typeQ=Q ₁+(1–)Q ₂ for some satisfying 01, whereQ ₁ is a probability measure, which is absolutely continuous with respect toP andQ ₂ is a one-point mass.     

Effect of outliers on the estimation of parameters

Summary The estimation of parameter in the type of distributionf(x)=b x ^{–1 /b} exp (–x ^b (/b),x>0, is considered, when several outliers of the type , ,r=1,2, ...,k, are present in the data. The estimates of as well as of 's are put in the closed form. Special cases, Weibull, Gamma and Exponential are considered for the case of single outlier. Actual estimates are calculated from the generated samples of size 2 and 3 for the Weibull and Exponential.