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Showing papers on "Principal component analysis published in 1968"


Journal ArticleDOI
TL;DR: In this article, a small-sample procedure is proposed for the interval estimation of the slope of the major axis of a bivariate normal distribution: the interval covers the slopes of all hypothetical major axes such that each is not significantly correlated with the corresponding minor axis.
Abstract: SUMMARY A small-sample procedure is proposed for the interval estimation of the slope of the major axis of a bivariate normal distribution: the interval covers the slopes of all hypothetical major axes such that each is not significantly correlated with the corresponding minor axis. It has been shown in a previous note (Jolicoeur [1965]) that, thanks to recent progress in the asymptotic theory of principal component analysis (Anderson [1963]), confidence limits can be calculated rather easily for the slope of the major axis of a bivariate normal distribution when one is studying a large sample. Upon further consideration of this problem the author has realized that a small-sample procedure can be based on the product-moment correlation coefficient and that its application is no more difficult than that of the large-sample method. Let us denote the sample covariance matrix of observed variates by S, the matrix of direction cosines of the principal axes of this sample covariance matrix by U, and the diagonal form of the sample covariance matrix by D:

48 citations


Journal ArticleDOI
TL;DR: The general procedure is shown to yield certain desirable invariance properties, with respect to transformations of the variables, that are desirable in the context of weighted linear combinations of variables.
Abstract: A general procedure is described for obtaining weighted linear combinations of variables. This includes as special cases, multiple regression weights, canonical variate analysis, principal components, maximizing composite reliability, canonical factor analysis, and certain other well-known methods. The general procedure is shown to yield certain desirable invariance properties, with respect to transformations of the variables.

47 citations


Journal ArticleDOI
TL;DR: In this paper, Tucker's three-mode principal components model is extended to a revision of Tucker's common factor analysis model, where the regression of the threemode manifest variates on variates used to select subpopulations is both linear and homoscedastic.
Abstract: Previous results of the application of Lawley's selection theorem to the common factor analysis model are extended to a revision of Tucker's three-mode principal components model. If the regression of the three-mode manifest variates on variates used to select subpopulations is both linear and homoscedastic, the two factor pattern matrices, the core matrix, and the residual variance-covariance matrix in the three-mode model can all be assumed to be invariant across subpopulations. The implication of this finding for simple structure is discussed.

42 citations




Journal ArticleDOI
TL;DR: In this article, the analysis of linear correlation in the presence of errors on all the variables is discussed, the two-variable case being treated in some detail, and some aspects of the problem of transforming between astronomical photometric systems are analyzed as an example.

20 citations


01 Sep 1968
TL;DR: The objective of this paper is to report on the application of principal component analysis to classification of local strains (open-pollinated varieties) of maize and to selection of breeding materials from them for use in hybrids and synthetic varieties.
Abstract: Collection of adapted local strains and introduction of exotic germ plasm for breedm:e has been frequently carried out in maize breeding. These strains ·were, in most cases, classified into groups on the basic of their origin and characteristics observed in introdllction fields, tested on their combining ability, and breeding materials ,,·ere selected from the strains. The objective of this paper is to report on the application of principal component analysis to classification of local strains (open-pollinated varieties) of maize and to selection of breeding materials from them for use in hybrids and synthetic varieties. The source materials in the present study were a series of the reports on the characteristics and the combining ability of Caribbean flint local strains collected from Fuji, Shikoku, and Kyushu in Japan. l\Iaize strains or collections were generally classified into strain group, varieties, or races based on observations on variations of many characters of a plant. So principal component analysis, a method of multivariate statistical analysis, was applied to the classification of the maize strains.

3 citations