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The Maxbet method is a generalized principal components analysis of a data set, where the group structure of the variables is taken into account. Similarly, 3-block[12,13] partial Maxdiff method is a generalization of covariance analysis, where only the covariances between blocks (1, 2) and (1, 3) are taken into account. The aim of this paper is to give the global maximum for the 2-block Maxbet and 3-block[12,13] partial Maxdiff problems by picking the best solution from the complete solution set for the multivariate eigenvalue problem involved. To do this, we generalize the characteristic polynomial of a matrix to a system of two characteristic polynomials, and provide the complete solution set of the latter via Sylvester resultants. Examples are provided. (Contains 2 tables.)

L. A. Goodman's loglinear formulation for bi-way contingency tables is extended to tables with or without missing cells and is used for exploratory purposes. Three-way tables and generalizations of correspondence analysis are deduced, and a generalized version of Goodman's algorithm is used to estimate scores in all cases. (Author/TJH)

In hydrology, one often needs to use goodness-of-fit tests to describe how well a statistical frequency model fits a set of observations. The two-parameter kappa (KAP2) distribution is a frequency model that has already shown useful hydrological applications. The Cramér-von Mises and the Anderson-Darling tests are among the most frequently used goodness-of-fit tests in statistical practice. To apply these tests to the KAP2 distribution, statistical tables of critical values are needed. Such tables already exist for various other statistical distributions, but have not yet been developed for KAP2. This paper fills the gap by developing such tables for the KAP2 distribution. These tables are based on large sample theory, but correction formulas are also provided that make them applicable to small samples. KAP2 and the generalized Pareto distribution (GPD) are two subfamilies of the four-parameter kappa distribution that have been used in extreme value hydrological applications in the past. A detailed example is given that shows the usefulness of the KAP2 model for fitting some types of extreme hydrological data, and another example is provided to show how KAP2 may be used as an alternative to the GPD in certain extreme value applications. [ABSTRACT FROM AUTHOR]

We present an analysis of a health survey data by multiple cor- respondence analysis (MCA) and multiple taxicab correspondence analysis (MTCA), MTCA being a robust L1 variant of MCA. The survey has one passive item, gender, and 22 active substantive items representing health services offered by municipal authorities; each active item has four answer categories: this service is used, never tried, tried with no access, non re- sponse. We show that the first principal MTCA factor is perfectly charac- terized by the sum score of the category this service is used over all service items. Further, we prove that such a sum score characterization always exists for any survey data. [ABSTRACT FROM AUTHOR]

The aim of this paper is the introduction of a new method for the numerical computation of the rank of a three-way array X ∈ RI×J×K over R. We show that the rank of a three-way array over R is intimately related to the real solution set of a system of polynomial equations. Using this, we present some numerical results based on the computation of Gr¨obner bases. Also, we show that for I = (K − 1)(J − 1) + 1 and 2 ≤ K ≤ J ≤ I, the rank for generic data has more than one rank value, and the minimum attained value is I. [ABSTRACT FROM AUTHOR]

The article investigates vocalization differences among three herds of harp seals using discriminant analysis. Based on the interpretation of the disco values of the variables and the apparent rates of classification of the three herds, it was revealed that the first factor of the multiple correspondence analysis discriminates best for multiple-element calls. This suggests that the Jan Mayen herd does not communicate with the other two herds although the latter two herds communicate with each other.