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.     

Confronto fra eventi condizionati di probabilità nulla nell'inferenza statistica Bayesiana

Dopo aver introdotto delle operazioni logiche fra eventicondizionati (che estendono opportunamente quelle usuali fra eventi), si definisce il concetto di iperprobabilità condizionata Si può così dare una interpretazione significativa della pseudodensità condizionata, introdotta da R. Scozzafava nell'inferenza statistica bayesiana.

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By a suitable extension of the usual algebra of events, logical operations forconditional events are introduced. This leads to a definition of conditional iperprobability, which is the natural tool for a sensible interpretation of the concept of conditional pseudodensity, introduced by R. Scozzafava in Bayesian statistical inference.

     

An Efficiency Comparison of European Banking Systems Operating under Different Environmental Conditions

The paper investigates the operating efficiency differences of a sample of commercial banks across 10 European countries. First, the paper analyzes the technical efficiency of each country sample following the basic Data Envelopment Analysis (DEA) model incorporating only banking variables. Then, a complete DEA model is introduced, incorporating environmental factors together with the banking variables of the basic model. The comparison between the two models shows that country-specific environmental conditions exercise a strong influence over the behavior of each country's banking industry.     

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.     

Interviewers,Interviewer Continuity,and Panel Survey Nonresponse

It is widely known that in practice, different interviewers have different response rates, though there has been no systematic examination of whether this is because of differences among interviewers or differences among those areas allocated to the interviewers (area effects), or both. Furthermore, the conventional wisdom in survey research suggests that it is advisable to have the same interviewers return to the same respondents in order to maintain good response rates in longitudinal surveys, though once again there has been very little documented experimental research to support this. This paper makes use of the interpenetrated sample design experiment in Wave 2 of the British Household Panel Study (BHPS) (i) to explore the effects of interviewers' background characteristics and years of experience on response rates, (ii) to identify and estimate the differential effects of interviewers on response rates and compare the magnitudes of area and interviewer effects, and (iii) to investigate the impact of interviewer continuity. The analysis is facilitated by the use of cross-classified multilevel modelling. The paper also looks at the issue of interviewer continuity qualitatively, through the impressions of the interviewers themselves.     

Estimation problems for rectangular distributions (or the taxi problem revisited)

The problem of estimating the unknown upper bound on the basis of a sample of sizen from a uniform or rectangular distribution on [0, ] has considerable interest. This or the analogous discrete version is variously known as the Taxi-problem or the German bomb (or Tank) problem and has a long history. The emphasis here is on estimation of through the lengths of the observed gaps or spacings which seem natural for this problem.     

Sulla dipendenza continua della probabilità di rovina dal caricamento dei premi

Si studia un modo di approssimare la probabilità di rovina relativa a un caricamento ₀ con le probabilità di rovina relative a una successione di caricamenti ( _k ) _k , che approssimano ₀ quandok tende all'infinito.

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Summary In this paper we study a way of approximating the probability of ruin related to a loading ₀, by the probabilities of ruin related of a sequence of loadings ( _k ) _k which «approximate» ₀ ask converges to infinity.

     

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 .     

Goodness-of-fit test with nuisance regression and scale

In the linear model Y _i = x _i + e _i, i=1,,n, with unknown (, ), {\open R}^p, >0, and with i.i.d. errors e ₁,,e _n having a continuous distribution F, we test for the goodness-of-fit hypothesis H ₀:F(e)F ₀(e/), for a specified symmetric distribution F ₀, not necessarily normal. Even the finite sample null distribution of the proposed test criterion is independent of unknown (,), and the asymptotic null distribution is normal, as well as the distribution under local (contiguous) alternatives. The proposed tests are consistent against a general class of (nonparametric) alternatives, including the case of F having heavier (or lighter) tails than F ₀. A simulation study illustrates a good performance of the tests. Received July 2001     

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.

     

Eine Verallgemeinerung des „Gesetzes seltener Ereignisse”

Zusammenfassung Beim bekannten Gesetz seltener Ereignisse betrachtet mane große Zahl unabhängiger Ereignisse, die jeweils mit der gleichen kleinen Wahrscheinlichkeit eintreten können. Unter geeigneten Annahmen ist die Zahl der eingetretenen Ereignisse näherungsweise poissonverteilt. [Vgl. z.B. Morgenstern, p. 39, 1968;Waerden, p. 47, 1957].Ein oft angegebenes Beispiel hierfür ist die Häufigkeitsverteilung von Unfällen, die jeweils nur eine Person oder ein Fahrzeug betreffen. In dieser Arbeit gehen wir von Unfällen mit zwei Beteiligten aus. Auf diese Weise erhält man eine Verallgemeinerung des Gesetzes seltener Ereignisse auf gewisse abhängige Ereignisse.Außerdem wird ein neuer Beweis für die allgemeine Formel der Momente der Poissonverteilung gegeben.Damit ist ein Grenzwertsatz für eine spezielle Folge schwach abhängiger Zufallsgrößen bewiesen.

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Summary The well-known law of rare events deals with a large number of independent events, each of which can occur with the same probability. Under suitable assumptions the number of events which occur has approximately a Poisson distribution. [CompareMorgenstern, p. 39, 1968;Waerden, p. 47, 1957].An example which is often used for illustration is the frequency distribution of accidents, in which only one car or one person is involved. In this paper we refer to accidents in which two parties are involved. This leads to a generalization of the law of rare events where cases of dependent events are concerned.In addition a new proof of the general formula as to the moments of Poisson distribution is given.This proves a limit theorem of weakly dependent random variables of a certain sequence.

     

Maximal asymptotic power and efficiency of two-sample tests based on generalized U-Statistics

In this article a systematic study is given of the asymptotic behavior of two-sample tests based on U-Statistics with arbitrary antisymmetric kernels . Besides the investigation under the hypothesis and under fixed alternatives we determine the local power as a function of as well as its maximizing value _opt. Moreover formulas for the asymptotic relative efficiency ARE(₂,₁) of the ₂-test with respect to the ₁-test are derived. It turns out that _opt also yields the most efficient test in the sense that ARE(_opt,)1 for all (admissible) kernels .     

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.     

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.     

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.     

On functionals of order statistics

Summary Let g_n be real functions,U _ni, 1in, the ordered sample ofn independentU(0,1) distributed random variables, andc _ni(), 1in, 01 be (known) real numbers,n=1, 2, ... The random quantity , 01, is studied. Based on a method proposed byShorack [1972] the main result is the weak convergence of to Gaussian processes, where , 01. The convergence is with respect to theSkorokhod [1956]-topologiesM ₂,M ₁ onD (I) and the -topology onC(I), depending on the conditions imposed on thec _ni().     

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.     

A curtailed test for the shape parameter of the Weibull distribution

Summary A procedure is proposed in this paper for testing the shape parameter, of the Weibull distribution. The test statistic which is based on the extremal quotient, possesses a monotone property which makes it possible for rejection earlier than the last planned observation of the null hypothesis,H ₀: =₀ when the alternative hypothesis isH _a: <₀ and early acceptance ofH ₀ whenH _a: >₀. The test being scale-free, does not require the scale parameter to be known.     

Hypocrisy pay

Emotional labor—putting on an act asrequired explicitly orimplicitly in work situations-is very often psychologically, emotionally, and mentally damaging to most employees. As for soldiers in wartime who receive combat pay, it is suggested that such employees be specially compensated for their emotional labor with hypocrisy pay. Another solution is to select only those who are immune to such stress for jobs involving emotional labor—an ideal that probably cannot be achieved in all cases. Another assessment is that such special compensation is unwarranted.     

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)).