Asymptotic expansions of the distribution of the estimator for the generalized partial correlation under nonnormality.

The generalized partial correlation is defined as a correlation between two variables, where the linear effects of common and unique third variables are partialed out from the two variables. The generalized partial correlation includes simple, partial, part/semipartial and bipartial correlations as special cases. The Edgeworth expansion of the distribution of the standardized sample coefficient for the generalized partial correlation is obtained up to order O(1/n) under nonnormality. Also asymptotic expansions of the distribution of the Studentized estimator are obtained using the Edgeworth expansion, Cornish-Fisher expansion and Hall\u27s method with variable transformation. As extensions, the results of multivariate cases or generalized partial set-correlations are given