Computer algebra application to the distribution of sample correlation coefficient

Let r be the sample correlation coefficient. In this paper, we clarify the role of computer algebra to obtain an asymptotic expansion for probability integrals of r. A key technique is to use a change of bases of the module of symmetric polynomials. We describe an algorithm for accomplishing it. We...

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Published inMathematics and computers in simulation Vol. 45; no. 1; pp. 23 - 32
Main Authors Nakagawa, Shigekazu, Niki, Naoto, Hashiguchi, Hiroki
Format Journal Article
LanguageEnglish
Published Elsevier B.V 31.01.1998
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Summary:Let r be the sample correlation coefficient. In this paper, we clarify the role of computer algebra to obtain an asymptotic expansion for probability integrals of r. A key technique is to use a change of bases of the module of symmetric polynomials. We describe an algorithm for accomplishing it. We derive the asymptotic cumulants of r in terms of population cumulants. An approximate distribution of r is also given.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0378-4754
1872-7166
DOI:10.1016/S0378-4754(97)00083-9