Journal of the Japan Statistical Society, Japanese Issue

AN ASYMPTOTIC THEORY OF CATEGORICAL PRINCIPAL COMPONENT ANALYSIS

Hideki Endo

1978 Volume 8 Issue 2 Pages 55-61
Published: 1978
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.8.55

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The aim of this paper is to show that the estimates for categorical principal component analysis follow asymptotically a normal distribution and to give the formulas of their asymptotic variances and covariances in parallel with our previous paper. The theorem proves to be only slightly different from those for categorical canonical correlation analysis. As an illustration the estimated values and their asymptotic standard deviations are computed for Stouffer and Toby's data dealing with the role conflict.

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OPTIMALITY OF MULTIDIMENSIONAL REPRESENTATION IN HAYASHI'S FOURTH METHOD OF QUANTIFICATION

Masashi Okamoto, Takafumi Isogai

1978 Volume 8 Issue 2 Pages 63-69
Published: 1978
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.8.63

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This paper first distinguishes two types of multidimensional representation in Hayashi's so-called “fourth method of quantification”, equilength representation and weighted representation. Next it presents three kinds of scale constraints of the coordinates and then shows that in the relation between the optimality problem and its solution there is a correspondence between the three kinds of scale constraints and the two types of multidimensional representation plus one-dimensional representation.

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A NOTE ON THE LEVEL OF SIGNIFICANCE OF THE PRELIMINARY TEST IN POOLING VARIANCES

Katuomi Hirano

1978 Volume 8 Issue 2 Pages 71-75
Published: 1978
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.8.71

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The problem of whether to pool two samples in variance estimation is often decided via a preliminary F-test. Since our ultimate objective is to estimate an unknown parameter, the theory of testing in this problem should be discussed as a part of the theory of estimation. If we consider the procedure of preliminary test estimation as an estimation procedure, the choice of the level of significance will not be arbitrary. The procedure of minimizing Akaike's information criterion uniquely determines the necessary significance levels of one-sided and two-sided preliminary tests.

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STABILIZING CONSTANTS AND ASYMPTOTIC BEHAVIORS OF THE EXTREME STATISTIC

Rinya Takahashi

1978 Volume 8 Issue 2 Pages 77-82
Published: 1978
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.8.77

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In this paper we consider stabilizing constants of the extreme statistic from a distribution function with a finite endpoint, and we treat some non-regular estimation problems based on asymptotic behaviors of the extreme statistic.

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