Numerical methods of statistics
Numerical methods of statistics
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Journal of Multivariate Analysis
Asymptotic expansion of the sample correlation coefficient under nonnormality
Computational Statistics & Data Analysis
Asymptotic cumulants of the parameter estimators in item response theory
Computational Statistics - Proceedings of DSC 2007
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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, asymptotic expansions of the distributions of the parameter estimators standardized by the population asymptotic standard errors up to order O(1/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.