四分相関係数の分布に関する漸近展開(一般セッション数学・統計(1))

概要

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Accurate distributions of the estimator of the tetrachoric correlation coefficient and, more generally, functions of sample proportions for the 2 by 2 contingency table are derived. The results are obtained given the definitions of the estimators even when some marginal cell(s) are empty. Then, local asymptotic expansions of the distributions of the parameter estimators standardized by the population asymptotic standard errors up to order O(l/n) and those of the studentized ones up to the order next beyond the conventional normal approximation are derived. The asymptotic results can be obtained in a much shorter computation time than the accurate ones. Numerical examples were used to illustrate advantages of the studentized estimator of Fisher's z transformation of the tetrachoric correlation coefficient. For the full result of this paper, see Ogasawara
2011-09-11