wgcm {comets}

Weighted Generalised covariance measure test

Description

Weighted Generalised covariance measure test

Usage

wgcm(
  Y,
  X,
  Z,
  reg_YonZ = "rf",
  reg_XonZ = "rf",
  reg_wfun = "rf",
  args_XonZ = NULL,
  args_wfun = NULL,
  frac = 0.5,
  B = 499L,
  coin = FALSE,
  cointrol = 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.

reg_YonZ

Character string or function specifying the regression for Y on Z. See ?regressions for more detail.

reg_XonZ

Character string or function specifying the regression for X on Z. See ?regressions for more detail.

reg_wfun

Character string or function specifying the regression for estimating the weighting function. See ?regressions for more detail.

args_XonZ

Additional arguments passed to reg_XonZ.

args_wfun

Additional arguments passed to reg_XonZ.

frac

Relative size of train split.

B

Number of bootstrap samples. Only applies if type = "max" is used.

coin

Logical; whether or not to use the coin package for computing the test statistic and p-value. The coin package computes variances with n - 1 degrees of freedom. The default is FALSE.

cointrol

List; further arguments passed to independence_test.

...

Additional arguments passed to reg_YonZ.

Details

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

Value

Object of class 'wgcm' 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

Weighted residuals for the X on Z regression.

References

Scheidegger, C., Hörrmann, J., & Bühlmann, P. (2022). The weighted generalised covariance measure. Journal of Machine Learning Research, 23(273), 1-68.

Examples

n <- 150
X <- matrix(rnorm(2 * n), ncol = 2)
colnames(X) <- c("X1", "X2")
Z <- matrix(rnorm(2 * n), ncol = 2)
colnames(Z) <- c("Z1", "Z2")
Y <- X[, 2]^2 + Z[, 2] + rnorm(n)
(wgcm1 <- wgcm(Y, X, Z))