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.

     

Una nuova caratterizzatione dell'ammissibilità nella teoria delle decisioni

In questo lavoro viene fornita una nuova caratterizzazione dell'ammissibilità attraverso un adeguato uso della nozione di ammissibilità parziale. Questa caratterizzazione consente di affrontare le questioni riguardanti la completezza della classe delle decisioni ammissibiliti sotto condizioni «maneggevoli». Fornisce inoltre un approccio unificante al problema della completezza che consente di derivare, come casi particolari, alcuni risultati già noti nella letteratura sull'argomento.

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In this paper a new characterization of admissibility is given for general decision problems. It is based on an adequate use of the notion of partial admissibility.A general decision problem is usually synthetized by a triplet (, , ) where is the states (or parameters) space, the set of available decisions and is a family of real valued functions defined on and expressing numerically the consequences of choosing when the state is . The set is regarded as a subset of the space of all real valued functions on endowed with the topology of pointwise convergence.As for as admissibility is concerned all the pertinent information about decisions are contained in the corresponding functionsW .This allows to introduce a notion of partial admissibility through the neigh-bourhoods of this topology. Admissibile decisions are then shown to be limits of monotone non increasing sequences of partially admissible decisions.Moreover this topological characterization allows to prove the completeness of classes of admissible decisions under acceptable systems of conditions which contain as special cases, known results in literature.

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Lavoro svolto nell'ambito del Gruppo Nazionale per l'Analisi Funzionale e le sue Applicazioni del C.N.R.     

Sub additive measures of relative information and inaccuracy

Summary In the study of information theoretic measures, additivity has been the basic requirement. However it is quite interesting to investigate the sub-additive measures. Starting from subadditivity for measures associated with a pair of distributions of a discrete random variable, it has been changed into an equality relation using another function of a pair of distributions., Under the sum property of the function and the measures, the relation is expressed in terms of a functional equation of which the most general complex solutions have been obtained. In terms of the real continuous solutions of the functional equation, the sub-additive measures of Relative information and Inaccuracy have been defined and characterized. Particular cases and simple properties particularly the convexities of some of these new measures have also been studied.     

Listen and learn

After making a solicitation, a lot can be gained by listening to a donor's questions. Do not simply answer the question. Consider why they asked it in the first place.     

Tax competition,uniform assessment,and the benefit principle

In previous discussions it has been argued that tax competition between local governments results in a tax burden on business that is less than the cost of public services for business and in suboptimal levels of public expenditures for residents. However, this conclusion has never been substantiated by a full theoretical treatment. Here a theoretical model of tax competition is developed between metropolitan areas, with labor perfectly immobile and two local public goods, one for residents and one for business. For “plausible” parameter values, numerical solutions of the optimality conditions are computed by means of a nonlinear programming algorithm.     

A model of public sector wage determination

The paper presents an empirical model of wage determination in the public sector that leads to the specification of a system of interrelated wage equations for municipal employees, which allows for occupational and geographic interdependence of wages. The model also considers the influence of public employee unions, municipal government form, and monopsony power of local governments on the wages of municipal employees. Several variants of the derived system of equations are estimated based upon 1967 cross-section data for 478 cities, and the policy implications of the results are discussed.     

Estimation of a non-invertible moving average process: The case of overdifferencing

The effect of differencing all of the variables in a properly specified regression equation is examined. Excessive use of the difference transformation induces a non-invertible moving average (MA) process in the disturbances of the transformed regression. Monte Carlo techniques are used to examine the effects of overdifferencing on the efficiency of regression parameter estimates, inferences based on these estimates, and tests for overdifferenccing based on the estimator of the MA parameter for the disturbances of the differences regression. Overall, the problem of overdifferencing is not serious if careful attention is paid to the properties of the disturbances of regression equations.     

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.