Asymptotic Expansions of the Distribution of the Estimator for the Generalized Partial Correlation Under Nonnormality |
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Authors: | Ogasawara Haruhiko |
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Affiliation: | 12.Department of Information and Management Science, Otaru University of Commerce, 3-5-21, Midori, Otaru, 047-8501, Japan ; |
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Abstract: | The generalized partial correlation is denned 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’s method with variable transformation. As extensions, the results of multivariate cases or generalized partial set-correlations are given. |
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