Asymptotic Expansions of the Distribution of the Estimator for the Generalized Partial Correlation Under Nonnormality | Zendy

Haruhiko Ogasawara | Zendy

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Asymptotic Expansions of the Distribution of the Estimator for the Generalized Partial Correlation Under Nonnormality

Author(s) -

Haruhiko Ogasawara

Publication year - 2008

Publication title -

behaviormetrika

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.507

H-Index - 8

eISSN - 1349-6964

pISSN - 0385-7417

DOI - 10.2333/bhmk.35.15

Subject(s) - mathematics , estimator , edgeworth series , partial correlation , studentized range , statistics , multivariate statistics , multivariate normal distribution , canonical correlation , asymptotic distribution , correlation , standard error , geometry

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

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