Applications of asymptotic theory to statistics such as covariances used in behaviormetrics

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Behaviormetrics is a technical term which has been used since 1970's as the advent of The Behaviormetric Society of Japan. The term indicates the quantitative methods used in the behavioral and social sciences including psychology, education, management and health sciences etc. The term covariance is an index in statistics corresponding to the strength of association between two variables. Since in practice, covariances are available only from finite samples, the values of observed covariances are subject to sampling variation. In this study, approximations of the distributions, which are more accurate than those used so far, for the sample indices like covariances, are derived using asymptotic theory developed in mathematical statistics.