Journal of the Japan Statistical Society, Japanese Issue

ON BALANCED ARRAYS OF 2 SYMBOLS, STRENGTH 2l, m CONSTRAINTS AND INDEX SET {μ₀, μ₁, …, μ_2l} WITH μ_l=0

Teruhiro Shirakura

1975 Volume 5 Issue 2 Pages 53-56
Published: 1975
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.5.53

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Consider a balanced array (“partially balanced” array, in the terminology of Chakravarti [1]) of 2 symbols, strength 2l, m constraints and index set {μ₀, μ₁, …, μ_2l}. Then it is shown that balanced arrays with μ_l=0 are simple. A necessary and sufficient condition for the existence of such balanced arrays is given.

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NECESSARY AND SUFFICIENT CONDITION FOR THE REDUCIBILITY OF ASSOCIATION SCHEMES

Kumaichi Kusumoto

1975 Volume 5 Issue 2 Pages 57-64
Published: 1975
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.5.57

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A necessary and sufficient condition for an m-class association scheme to be reducible is given in terms of the characteristic matrix of the association scheme. A method of constructing a new series of association schemes which are called two level m-factorial association schemes is also shown.

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SOME MODIFIED MONTE CARLO METHOD TO SOLVE NON-LINEAR OPTIMIZATION PROBLEMS

Masaaki Taguri

1975 Volume 5 Issue 2 Pages 65-76
Published: 1975
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.5.65

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ON MONETARY INTEREST FROM A PROBABILISTIC POINT OF VIEW

Ryoichiro Sato

1975 Volume 5 Issue 2 Pages 77-85
Published: 1975
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.5.77

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A new approach is made to the theory of monetary interest from a point of view of probability theory.

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Asymptotic Expansions for the General Distributions of Test Statistics in Multivariate Analysis

The Methods in the Recent Development, I

Minoru Siotani

1975 Volume 5 Issue 2 Pages 87-103
Published: 1975
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.5.87

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This is a survey paper on various methods developed in recent years for obtaining asymptotic expansions for the nonnull distributions of multivariate test statistics. In Part I, two methods are discussed: (1) one by the Taylor expansion, including studentization; (2) one by the expansion of the exact characteristic functions using the formulae for weighted sums of zonal polynomials. Part II will be given in the separate paper in the next issue, and contain (3) the method based on the system of partial differential equations satisfied by the hypergeometric functions, (4) the method by an expansion of test statistics in terms of normal variates, and (5) the method based on the representation of an orthogonal matrix by a skew symmetric matrix. In the discussion, emphasis is on the basic idea of the deriving techniques, and details of computation and final forms of individual asymptotic expansions explained as examples to clarify the idea are omitted; appropriate references, however, are given.

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[title in Japanese]

[in Japanese]

1975 Volume 5 Issue 2 Pages 105-117
Published: 1975
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.5.105

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