Journal of the Japanese Society of Computational Statistics

DISTRIBUTION OF THE SAMPLE CORRELATION COEFFICIENT FOR NONNORMAL POPULATIONS

Shigekazu Nakagawa, Naoto Niki

1992 Volume 5 Issue 1 Pages 1-19
Published: 1992
Released on J-STAGE: December 09, 2009

DOIhttps://doi.org/10.5183/jjscs1988.5.1

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Let r be the correlation coefficient formed from a sample of size n from a bivariate population with the distribution function F. Assume that F has finite cumulants and product cumulants of total order eight. This paper presents the approximate cumulants of the distribution of r up to the fourth order. The Edgeworth expansion for probability integrals and the Cornish-Fisher inverse expansion for percentiles of order 1/n are also given. A numerical experiment demonstrates the substantial effects in approximation of using the higher order terms.

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A CLUSTERING ALGORITHM FOR DETECTING INFLUENTIAL SUBSETS IN MULTIVARIATE METHODS

Sung Ho Moon, Kikuo Yanagi, Yutaka Tanaka

1992 Volume 5 Issue 1 Pages 21-31
Published: 1992
Released on J-STAGE: December 09, 2009

DOIhttps://doi.org/10.5183/jjscs1988.5.21

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A clustering algorithm is proposed for detecting influential subsets of observations in multivariate methods such as principal component analysis, exploratory factor analysis and covariance structure analysis where the influence functions have been derived. It makes clusters hierarchically by optimizing a criterion defined by a specified aspect of influence among some different aspects such as the influence on the estimate, on its precision and on the goodness of fit. A numerical example is given to show the usefulness of the proposed method in maximum likelihood factor analysis (MLFA).

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THE ORTHOGONAL PROJECTION MATRIX FOR THE UNBALANCED FACTORIAL DESIGN

Byung Chun Kim, Jong Tae Park

1992 Volume 5 Issue 1 Pages 33-42
Published: 1992
Released on J-STAGE: December 09, 2009

DOIhttps://doi.org/10.5183/jjscs1988.5.33

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The design matrix X for an unbalanced factorial design can be expressed as a product of two matrices T and X_o, where T is replication matrix and X_o is the corresponding balanced design matrix. We suggest an efficient method for computing the orthogonal projection matrix P_X=X(X'X)-X' for an unbalanced model y=Xβ+e using the nonzero eigenvalues and eigenvectors of X_o'X_o. Also we can easily find a regular rule for the nonzero eigenvalues and the corresponding eigenvectors.

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MEASURE OF DEPARTURE FROM SYMMETRIC ASSOCIATION IN SQUARE CONTINGENCY TABLES WITH ORDERED CATEGORIES

Sadao Tomizawa

1992 Volume 5 Issue 1 Pages 43-49
Published: 1992
Released on J-STAGE: December 09, 2009

DOIhttps://doi.org/10.5183/jjscs1988.5.43

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A measure is proposed to represent the degree of departure from symmetric association in square contingency tables with ordered categories. The measure is expressed by using the minimum Euclidean distance based on the local odds-ratios. It would be useful when one wants to use a single summary measure to measure distance of the local odds-ratios from symmetry of association.

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ON THE PERMUTATION DISTRIBUTION OF THE RANK PRODUCT-MOMENT STATISTIC

Osamu Sugano, Shingo Watadani

1992 Volume 5 Issue 1 Pages 51-63
Published: 1992
Released on J-STAGE: December 09, 2009

DOIhttps://doi.org/10.5183/jjscs1988.5.51

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Under the null hypothesis of independency, the exact mean and variance of Wald and Wolfwitz statistic W_N are calculated. For the case of equally likely permutations, tables of the exact distribution of W are given for 6≤N≤13 and Monte Carlo approximate results are given for 14≤N≤30. The simple normal approximation may be adequate for N≥31. Some properties of W_N are given and a serial correlation test based on W_N is applied to a small-sample example.

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AN EFFICIENT ALGORITHM FOR THE NONPARAMETRIC REGRESSION ESTIMATION

Byung Gook Lee, Byung Chun Kim

1992 Volume 5 Issue 1 Pages 65-73
Published: 1992
Released on J-STAGE: December 09, 2009

DOIhttps://doi.org/10.5183/jjscs1988.5.65

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Most bandwidth selectors in nonparametric kernel regression estimation are based on minimization of some function of h, which is related to the resubstitution estimate of the prediction error. But this method consumes large amounts of computer time. This article concerns an efficient computational algorithm for this method when the kernel is symmetric and polynomial functions.

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Abstracts of Bulletin of the Computational Statistics of Japan

1992 Volume 5 Issue 1 Pages 75-77
Published: 1992
Released on J-STAGE: December 09, 2009

DOIhttps://doi.org/10.5183/jjscs1988.5.75

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Abstracts of Bulletin of the Computational Statistics of Japan

1992 Volume 5 Issue 1 Pages 78-80
Published: 1992
Released on J-STAGE: December 09, 2009

DOIhttps://doi.org/10.5183/jjscs1988.5.78

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Papers presented in the 6th Annual Meeting of the Society

1992 Volume 5 Issue 1 Pages 81-83
Published: 1992
Released on J-STAGE: December 09, 2009

DOIhttps://doi.org/10.5183/jjscs1988.5.81

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