gcm {comets}

Generalised covariance measure test using random forests

Description

Generalised covariance measure test using random forests

Usage

gcm(
  Y,
  X,
  Z,
  alternative = c("two.sided", "less", "greater"),
  reg_YonZ = "rf",
  reg_XonZ = "rf",
  args_XonZ = NULL,
  ...
)

Arguments

Y

Vector of response values. Can be supplied as a numeric vector or a single column matrix.

X

Matrix or data.frame of covariates.

Z

Matrix or data.frame of covariates.

alternative

A character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less"

reg_YonZ

Character string or function specifying the regression for Y on Z.

reg_XonZ

Character string or function specifying the regression for X on Z.

args_XonZ

Additional arguments passed to reg_XonZ.

...

Additional arguments passed to reg_YonZ

Details

The generalised covariance measure test tests whether the conditional covariance of Y and X given Z is zero.

Value

Object of class 'gcm' and 'htest' with the following components:

statistic

The value of the test statistic.

p.value

The p-value for the hypothesis

parameter

In case X is multidimensional, this is the degrees of freedom used for the chi-squared test.

hypothesis

String specifying the null hypothesis .

null.value

String specifying the null hypothesis.

method

The string "Generalised covariance measure test".

data.name

A character string giving the name(s) of the data.

rY

Residuals for the Y on Z regression.

rX

Residuals for the X on Z regression.

References

Rajen D. Shah, Jonas Peters "The hardness of conditional independence testing and the generalised covariance measure," The Annals of Statistics, 48(3), 1514-1538. doi: 10.1214/19-aos1857

Examples

X <- matrix(rnorm(3e2), ncol = 2)
colnames(X) <- c("X1", "X2")
Z <- matrix(rnorm(3e2), ncol = 2)
colnames(Z) <- c("Z1", "Z2")
Y <- rnorm(150) # X[, 2] + Z[, 2] + rnorm(150)
(gcm1 <- gcm(Y, X, Z))