2011 年 38 巻 2 号 p. 153-168
Asymptotic expansions of the distributions of the sample polyserial correlation coefficients and associated parameter estimators are derived up to order O(1/N) when the estimators are obtained by full maximum likelihood. The asymptotic results are given under the assumption of multivariate normality for several observed continuous variables and a single unobserved variable underlining the corresponding ordered categorical variable. Asymptotic expansions of the distributions of the pivotal statistics studentized by using the estimate of the information matrix are obtained up to the order next beyond the conventional normal approximation. Numerical examples with simulations are shown in order to illustrate the accuracy of the asymptotic results in finite samples.
