On the Estimation of Polychoric Correlations and their Asymptotic Covariance Matrix

A general theory for parametric inference in contingency tables is outlined. Estimation of polychoric correlations is seen as a special case of this theory. The asymptotic covariance matrix of the estimated polychoric correlations is derived for the case when the thresholds are estimated from the univariate marginals and the polychoric correlations are estimated from the bivariate marginals for given thresholds. Computational aspects are also discussed.