MINTauto {IndepTest}

MINTauto

Description

Performs an independence test without knowledge of either marginal distribution using permutations and using a data-driven choice of k.

Usage

MINTauto(x, y, kmax, B1 = 1000, B2 = 1000)

Arguments

x

The n \times d_{X} data matrix of the X values.

y

The response vector of length n \times d_{Y} data matrix of the Y values.

kmax

The maximum value of k to be considered for estimation of the joint entropy H(X,Y).

B1

The number of repetitions used when choosing k, set to 1000 by default.

B2

The number of permutations to use for the final test, set at 1000 by default.

Value

The p-value corresponding the independence test carried out and the value of k used.

References

Berrett, T. B. and Samworth R. J. (2017). “Nonparametric independence testing via mutual information.” ArXiv e-prints. 1711.06642.

Examples

# Independent univariate normal data
x=rnorm(1000); y=rnorm(1000);
MINTauto(x,y,kmax=200,B1=100,B2=100)
# Dependent univariate normal data
library(mvtnorm)
data=rmvnorm(1000,sigma=matrix(c(1,0.5,0.5,1),ncol=2))  
MINTauto(data[,1],data[,2],kmax=200,B1=100,B2=100)
# Dependent multivariate normal data
Sigma=matrix(c(1,0,0,0,0,1,0,0,0,0,1,0.5,0,0,0.5,1),ncol=4)
data=rmvnorm(1000,sigma=Sigma)
MINTauto(data[,1:3],data[,4],kmax=50,B1=100,B2=100)