Optimale Aufteilung des Stichprobenumfangs bei mehreren Merkmalen

Zusammenfassung Es wird gezeigt, daß sich das vonNeyman undTschuprow für ein einziges Merkmal gelöste Problem der optimalen Aufteilung des Stichprobenumfangs auf vorgegebene Schichten auf ein nichtlineares Programm mit linearen Restriktionen und nichtlinearer Zielfunktion zurückführen läßt. Auf Grund der Konvexitätseigenschaft der Zielfunktion ergibt sich, daß das Minimum der Zielfunktion (Minimum der Streuung des Stichprobenmittels ) stets eindeutig ist. Der beiNeyman undTschuprow mögliche Fall, daß sich in derh-ten Schicht ein Stichprobenumfang ergibt, der größer als der Umfang in der Gesamtheit ist, kann hier nicht auftreten.Durch Einführung einer verallgemeinerten Streuung wird das Problem der optimalen Aufteilung bei vorgegebener Schichtung imk-dimensionalen Merkmalsraum aufk Merkmale verallgemeinert. Es wird gezeigt, daß diese verallgemeinerte Streuung (=Zielfunktion eines nichtlinearen Programms) im allgemeinen nicht über dem ganzen konvexen Bereich der zulässigen Lösungen konvex (von unten) ist. Ein Teilbereich des zulässigen Bereichs, über dem die Zielfunktion konvex ist, wird angegeben. Schließlich werden hierzu vergleichende Ergebnisse gebracht.     

Fit performance of several programs used for non-linear least squares problems

Seven computerprograms for non-linear regression or curve fitting problems are compared. The comparison of the programs, running in different computing centra, is restricted to the fit performance. Six model functions are fitted according to the least squares criterion to data series, arising from practical work. The special least squares minimization programs turned out to be better suited for these problems than general optimizing programs.     

A Stochastic Frontier Production Function with Flexible Risk Properties

This paper considers a stochastic frontier production function which has additive, heteroscedastic error structure. The model allows for negative or positive marginal production risks of inputs, as originally proposed by Just and Pope (1978). The technical efficiencies of individual firms in the sample are a function of the levels of the input variables in the stochastic frontier, in addition to the technical inefficiency effects. These are two features of the model which are not exhibited by the commonly used stochastic frontiers with multiplicative error structures.An empirical application is presented using cross-sectional data on Ethiopian peasant farmers. The null hypothesis of no technical inefficiencies of production among these farmers is accepted. Further, the flexible risk models do not fit the data on peasant farmers as well as the traditional stochastic frontier model with multiplicative error structure.     

Taxation and the stock market valuation of capital gains and dividends: Theory and emphirical results

Dividends seem to be more heavily taxed than capital gains. Why then do corporations pay dividends rather than repurchasing shares or retaining earnings? Either corporations are not acting in the interests of shareholders, or else shareholders desire dividends sufficiently for nontax reasons to offset the tax effect.In this paper, we measure the relative valuation of dividends and capital gains in the stock market, using a variant of the capital asset pricing model. We find that dividends are not valued differently systematically from capital gains. This finding is consistent with share price maximization by firms but inconsistent with the fact that most shareholderspay a heavier tax on dividends.We also show that the relative value of dividends provides an indirect measure of a marginal Tobin's q. The measured value of dividends relative to capital gains tends to be higher during prosperous periods, as is consistent with this interpretation. We hope that this time series on a marginal Tobin's q will prove to be useful in forecasting the rate of investment.     

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.     

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.

     

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.