estats (version 1.0)

Hypothesis test for the distance correlation with high dimensional matrices: Hypothesis test for the distance correlation with high dimensional matrices

Description

Hypothesis test for the distance correlation with high dimensional matrices.

Usage

dcor.ttest(x, y, logged = FALSE)

Value

A vector with 4 elements, the bias corrected distance correlation, the degrees of freedom, the test statistic and its associated p-value.

Arguments

x

A numerical matrix.

y

A numerical matrix (of the same dimensions).

logged

Do you want the logarithm of the p-value to be returned? If yes, set this to TRUE.

Author

Manos Papadakis

R implementation and documentation: Michail Tsagris <[e-mail]> and Manos Papadakis <[e-mail]>.

Details

The bias corrected distance correlation is used. The hypothesis test is whether the two matrices are independent or not. Note, that this test is size correct as both the sample size and the dimensionality goes to infinity. It will not have the correct type I error for univariate data or for matrices with just a couple of variables.

References

G.J. Szekely, M.L. Rizzo and N. K. Bakirov (2007). Measuring and Testing Independence by Correlation of Distances. Annals of Statistics, 35(6): 2769--2794.

Szekely G. J. and Rizzo M. L. (2023). The Energy of Data and Distance Correlation. Chapman and Hall/CRC.

See Also

dcov, edist

Examples

x <- as.matrix(iris[1:50, 1:4])
y <- as.matrix(iris[51:100, 1:4])
dcor.ttest(x, y)