gcm.test {GeneralisedCovarianceMeasure}

Test for Conditional Independence Based on the Generalized Covariance Measure (GCM)

Description

Test for Conditional Independence Based on the Generalized Covariance Measure (GCM)

Usage

gcm.test(X, Y, Z = NULL, alpha = 0.05, regr.method = "xgboost",
  regr.pars = list(), plot.residuals = FALSE, nsim = 499L,
  resid.XonZ = NULL, resid.YonZ = NULL)

Arguments

X

A (nxp)-dimensional matrix (or data frame) with n observations of p variables.

Y

A (nxp)-dimensional matrix (or data frame) with n observations of p variables.

Z

A (nxp)-dimensional matrix (or data frame) with n observations of p variables.

alpha

Significance level of the test.

regr.method

A string indicating the regression method that is used. Currently implemented are "gam", "xgboost", "kernel.ridge". The regression is performed only if not both resid.XonZ and resid.YonZ are set to NULL.

regr.pars

Some regression methods require a list of additional options.

plot.residuals

A Boolean indicating whether some plots should be shown.

nsim

An integer indicating the number of bootstrap samples used to approximate the null distribution of the test statistic.

resid.XonZ

It is possible to directly provide the residuals instead of performing a regression. If set to NULL, the regression method specified in regr.method is used.

resid.YonZ

It is possible to directly provide the residuals instead of performing a regression. If set to NULL, the regression method specified in regr.method is used.

Value

The function tests whether X is conditionally independent of Y given Z. The output is a list containing

• p.value: P-value of the test.

• test.statistic: Test statistic of the test.

• reject: Boolean that is true iff p.value < alpha.

References

Please cite the following paper. Rajen D. Shah, Jonas Peters: "The Hardness of Conditional Independence Testing and the Generalised Covariance Measure" https://arxiv.org/abs/1804.07203

Examples

set.seed(1)
n <- 250 
Z <- 4*rnorm(n) 
X <- 2*sin(Z) + rnorm(n)
Y <- 2*sin(Z) + rnorm(n)
Y2 <- 2*sin(Z) + X + rnorm(n)
gcm.test(X, Y, Z, regr.method = "gam")
gcm.test(X, Y2, Z, regr.method = "gam")