Journal of the Japan Statistical Society, Japanese Issue

AN ASYMPTOTIC THEORY OF CATEGORICAL CANONICAL CORRELATION ANALYSIS

Masashi Okamoto, Hideki Endo

1974 Volume 5 Issue 1 Pages 1-8
Published: 1974
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.5.1

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When the categorical canonical correlation analysis studied in the authors' previous paper is applied to a set of real data, it is desirable to have some idea about the reliability of the estimates obtained, scores, weights and eigenvalues. The purpose of this paper is to show by means of the δ-method that the estimates follow asymptotically a normal distribution with the true values of the parameters as the means and also to find the formulas for the asymptotic variances and covariances of the estimates. As an illustration the estimated values and their asymptotic variances are computed for Hayashi's data dealing with the label preference problem.

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On the Representation Method of Multiple Correlation by Pattern of Connected Vectors

Kazumasa Wakimoto, Masaaki Taguri

1974 Volume 5 Issue 1 Pages 9-24
Published: 1974
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.5.9

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Distribution and Migration of Population

Keisuke Suzuki, Saburo Yasuda

1974 Volume 5 Issue 1 Pages 25-36
Published: 1974
Released on J-STAGE: August 24, 2009

DOIhttps://doi.org/10.11329/jjss1970.5.25

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This article reviews some statistical models on the distribution and migration rules of population which appeared in the representative literatures. Topics delt with here are as follows: (1) the lognormal or truncated lognormal distributions of the city population which are derived from the central limit theorem and some other bases, (2) several explanatory and modified models on the rank-size rule existing between the rank of a city in population and its population, (3) the gravity models on migration with rationales in terms of probability and information theories including the concept of entropy, and (4) the Markov chain models as a stochastic process on the population mobility. Brief discussions on the Colin Clark's law of urban population density, the opportunity models of migration and the rule of the shortest distance between cities are also included.

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[title in Japanese]

[in Japanese], [in Japanese], [in Japanese], [in Japanese]

1974 Volume 5 Issue 1 Pages 49-52
Published: 1974
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.5.49

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