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  1. 2 Przegląd Statystyczny

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  1. 2 Westa M.

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  1. 2 2008

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1

A METHOD FOR CONSTRUCTING VECTORS OF OBSERVATIONS ON VARIABLES WITH THE GIVEN CORRELATION MATRIX

100%
Westa M.
Przegląd Statystyczny
|
2008
|
vol. 55
|
issue 3
61-70
EN
In the paper, it was proposed a method for constructing the vectors of observations on the variables, such that the given positive semi-definite symmetric matrix, which has the following properties: - all elements on the main diagonal are units; - all elements outside the main diagonal are not greater than one in absolute value, is their correlation matrix.
2

A NECESSARY AND SUFFICIENT CONDITION FOR A SYMMETRIC MATRIX TO BE A CORRELATION MATRIX

100%
Westa M.
Przegląd Statystyczny
|
2008
|
vol. 55
|
issue 3
33-46
EN
Borowiecki, Kolupa and Kaliszyk (1984) and Dudek (2003) proposed methods in which the generalised Hellwig's inequality is used for verifying that a symmetric matrix, which has the following properties: (1) - all elements on the main diagonal are units; (2) -all elements outside the main diagonal are not greater than one in absolute value, is a correlation matrix of certain variables. The authoress (see forthcoming paper) showed that this verification procedure may improperly indicate the correlation matrices. The theorems proved in the present paper define various forms of the necessary and sufficient condition for a symmetric matrix with properties (1)-(2) to be a correlation matrix. Among others things, it was shown that any symmetric 3x3 matrix with properties (1)-(2) is a correlation matrix if and only if its determinant is non-negative. Some results obtained generalize those given by Hauke and Pomianowska (1987) for correlation pair.
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