Chatterjee Correlation Coefficient

This function computes the Chatterjee coefficient between two vectors x and y

% This function computes the Chatterjee coefficient between two vectors x and y. If only one coefficient is computed it can be used to test independence using a Monte Carlo

% permutation test or through an asymptotic approximation test.

% x Vector of numeric values in the first coordinate.

% y Vector of numeric values in the second coordinate.

% pvalue Whether or not to return the p-value of rejecting independence, if TRUE the

% function also returns the standard deviation of xi.

% ties Do we need to handle ties? If ties=TRUE the algorithm assumes that the data

% has ties and employs the more elaborated theory for calculating s.d. and P-value.

% Otherwise, it uses the simpler theory. There is no harm in putting ties = TRUE

% even if there are no ties.

% method If method = "asymptotic" the function returns P-values computed by the asymptotic theory. If method = "permutation", a permutation test with nperm permutations is employed to estimate the P-value. Usually, there is no need for the

% permutation test. The asymptotic theory is good enough.

% nperm In the case of a permutation test, nperm is the number of permutations to do.

% In the case pvalue=FALSE, function returns the value of the xi coefficient, if the input is a matrix, a

% matrix of coefficients is returned. In the case pvalue=TRUE is chosen, the function returns a list:

% xi The value of the xi coefficient.

% sd The standard deviation.

% pval The test p-value.

% References

% Chatterjee, S. (2020) <arXiv:1909.10140>.