Generalized, Partial and Canonical Correlation Coefficients

Hrishikesh Vinod

Computational Economics, 2022, vol. 60, issue 4, No 12, 1479-1506

Abstract: Abstract We use a simple example to show that Pearson’s correlation matrix R can underestimate the true dependence between two variables when nonlinearities are present by as much as 83%, compared to the newer and easy to compute $$R^*$$ R ∗ in Vinod (Commun Statist Simul Comput 46(6):4513–4534, 2017, https://doi.org/10.1080/03610918.2015.1122048 ). We include intuitive expository discussion of nonparametric kernel methods needed by $$R^*$$ R ∗ with graphs and examples. We illustrate how partial correlation coefficients based on R can underestimate the nonlinear effect of a confounding variable, compared to those from the newer $$R^*$$ R ∗ . This paper develops an entirely new generalization of Hotelling’s canonical correlations based on nonlinear nonparametric pairwise dependencies of $$R^*$$ R ∗ . An example illustrates how traditional methods can underestimate the joint dependence by 266%.

Keywords: Kernel regression; Grid interpolation; Nonparametric estimation; Lagrangian; Dependence measures (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10614-021-10190-x

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