Tests of Partial Correlation in a Linear Model

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Abstract
Two asymptotically distribution-free tests of partial correlation in a trivariate linear model are proposed. The model includes two nuisance parameters, and the tests use modified varsions of Kendall's and Spearman's correlation coefficients for transformed values of the observations, where the transformation is chosen to eliminate the nuisance parameters by using consistent estimators of them. Some arguments about the asymptotic properties of the statistics and computer simulation results are given.

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