On minimum distance estimators for unimodal densities

It is shown that minimum distance estimators for families of unimodal densities are always consistent; the rate of convergence is indicated. An algorithm is proposed for computing the minimum distance estimator for the family of all unimodal densities. References are given to the maximum likelihood method and the kernel method.     

Probenahme vom Band

Ohne Zusammenfassung     

Economie en vooruitgangsidee

Summary The object of this article is the relation between economic science and the idea of progress in western civilization. That relation can clearly be observed in classical economic theory (influenced by the Enlightment) and the modern theory of growth (Golden Age Economics). The author rejects any identification of economic progress with an unlimited increase of GNP. He proposes a link between the idea of economic progress and the divine mandate of stewardship, which implies that the inter-subjective scarcity of non-renewable resources and environmental factors should constantly be taken into account. He concludes with some remarks about economic growth as a goal of economic policy.

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Rede uitgesproken bij de aanvaarding van het ambt van gewoon hoogleraar aan de Vrije Universiteit op 10 maart 1972.     

Identification and Measurement of Australian Consumer Sentiment

This article was prepared by Dr L. V. Defris and J. S. McDonnell of the Institute research staff. The authors wish to thank Professor R. F. Henderson and Dr P. J. Sheehan for their helpful comments.     

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.