Summary

As an application of tests of general linear hypotheses methods are presented for testing the equality of coefficient matrices of linear restrictions with normal univariate and multivariate regression models. Geometrical interpretations of the results are given. The present paper generalizes some of the earlier results obtained byTocher, andBennett.

This paper describes an algorithm for determining the best subset of k variables in regression problems using any L_P-norm with 1≤p<∞. The procedure is based on partial enumeration. It also makes a suggestion for finding the equation with least prediction error.

Summary

For regression problems where observations may be taken at points in a set X which does not coincide with the set Y on which the regression function is of interest, we consider the problem of finding a design (allocation of observations) which minimizes the maximum over Y of the variance function (of estimated regression). Specific examples are calculated for one-dimensional polynomial regression when Y is much smaller than or much larger than X. A related problem of optimum estimation of two regression coefficients is studied. This paper contains proofs of results first announced at the 1962 Minneapolis Meeting of the Institute of Mathematical Statistics. No prior knowledge of design theory is needed to read this paper.

Zusammenfassung

Auf der Basis eines log-linearen hierarchischen Modells wird das Kontingenztableau zweier qualitativer Merkmale mit Hilfe von Assoziationsmaßen ausgewertet:

Unter multinomialen Verteilungsannahmen liefert die Maximum-Likelihood-Schätzmethode die Haupt- und bivariaten Interaktionseffekte. Diese i.a. unübersichtliche Information wird mit Hilfe bekannter Assoziationsmaße verdichtet. Deren asymptotisches Verhalten wird an einem empirischen Datensatz demonstriert.

Summary

This paper develops for the several sample problem the notions of a parametric family of non-parametric alternatives. In section two we give a detailed characterization of the class of all locally most powerful rank order tests for testing the hypothesis of equality of several continuous distributions. In section three we show that the class of all locally most powerful rank order tests coincides with the class of all locally least powerful tests. In section four we consider a multiple decision problem with non-parametric slippage alternatives and characterize the class of all locally best symmetric decision procedures based on rank orders.