XICOR (version 0.4.1)

genxicor: Compute the generalized cross rank increment correlation coefficient gxi.

Description

This function computes the generalized xi coefficient between two matrices xmat and ymat. There is a limitation on the size of the matrices, for the time being, xmat and ymat can only have 31 columns. If they are wider than 31, there is the option of using a dimension reduction technique to bring the number of columns down to 31, the first 31 components are then used. The function encodes the data using a binary expansion and then calls xicor on the vectors, so some of the arguments relevant for xicor can be specified, such as pvalue.

Usage

genxicor(xmat, ymat)

Value

Function returns the value of the genxi coefficient. Since by default the option pvalue=TRUE is chosen, the function returns a list:

sd

The standard deviation.

pval

The test p-value.

Arguments

xmat

Matrix of numeric values in the first argument.

ymat

Matrix of numeric values in the second argument.

Author

Sourav Chatterjee, Susan Holmes

References

Chatterjee, S. (2022) <arXiv:2211.04702>

Examples

example_joint_calc = function(n,x=runif(n),y=runif(n),ep=runif(n)) {
u = (x + y + ep) %% 1
v = ((x + y)/2 + ep) %% 1
w = (4*x/3 + 2*y/3 + ep) %% 1
z = (2*x/3 + y/3 + ep) %% 1
q = cbind(u,v,w,z)
p = cbind(x,y)
c1 = genxicor(u, p)
c2 = genxicor(v, p)
c3 = genxicor(w, p)
c4 = genxicor(z, p)
c5 = genxicor(q, p)
return(list(marg1 = c1$xi, marg2 = c2$xi, marg3 = c3$xi, 
marg4 = c4$xi, joint = c5$xi, p1 = c1$pval, p2 = c2$pval, p3 = c3$pval,
p4 = c4$pval, p5 = c5$pval))
}
result1 <- example_joint_calc(n=10)