Partial distance correlation and covariance

Description

Partial distance correlation pdcor, pdcov, and tests.

Usage

  pdcov.test(x, y, z, R)
  pdcor.test(x, y, z, R)
  pdcor(x, y, z)
  pdcov(x, y, z)

Arguments

Details

pdcor(x, y, z) and pdcov(x, y, z) compute the partial distance correlation and partial distance covariance, respectively, of x and y removing z.

A test for zero partial distance correlation (or zero partial distance covariance) is implemented in pdcor.test, and pdcov.test.

If the argument is a matrix, it is treated as a data matrix and distances are computed (observations in rows). If the arguments are distances or dissimilarities, they must be distance (dist) objects. For symmetric, zero-diagonal dissimilarity matrices, use as.dist to convert to a dist object.

Value

Each test returns an object of class htest.

Author(s)

Maria L. Rizzo mrizzo @ bgsu.edu and Gabor J. Szekely

References

Szekely, G.J. and Rizzo, M.L. (2014), Partial Distance Correlation with Methods for Dissimilarities. Annals of Statistics, Vol. 42 No. 6, 2382-2412.

Examples

  n = 30
  R <- 199

  ## mutually independent standard normal vectors
  x <- rnorm(n)
  y <- rnorm(n)
  z <- rnorm(n)

  pdcor(x, y, z)
  pdcov(x, y, z)
  pdcov.test(x, y, z, R=R)
  print(pdcor.test(x, y, z, R=R))


if (require(MASS)) {
  p = 4
  mu <- rep(0, p)
  Sigma <- diag(p)

  ## linear dependence
  y <- mvrnorm(n, mu, Sigma) + x
  print(pdcov.test(x, y, z, R=R))

  ## non-linear dependence
  y <- mvrnorm(n, mu, Sigma) * x
  print(pdcov.test(x, y, z, R=R))
  }