Covariance Computations Between Pairs of Distances (Independent Case)

Computes covariance matrix entries and associated alpha, beta and gamma quantities defined in Aw, Spence and Song (2021), assuming the \(P\) features of the dataset \(\mathbf{X}\) are independent.

getCov(X, p = 2)

Arguments

X

The binary or real matrix

p

The power \(p\) of \(l_p^p\), i.e., \(||x||_p^p = (x_1^p+...x_n^p)\)

Value

The three distinct entries of covariance matrix, \((\alpha, \beta, \gamma)\)

Details

This is used in the large \(P\) asymptotics of the permutation test.

Dependencies: buildReverse, getLpDistance