cdcov.test {cdcsis}

Conditional Distance Covariance Independence Test

Description

Performs the nonparametric conditional distance covariance test for conditional independence assumption

Usage

cdcov.test(
  x,
  y,
  z,
  num.bootstrap = 99,
  width,
  distance = FALSE,
  index = 1,
  seed = 1,
  num.threads = 1
)

Arguments

x

a numeric vector, matrix, or dist object

y

a numeric vector, matrix, or dist object

z

z is a numeric vector or matrix. It is the variable being conditioned.

num.bootstrap

the number of local bootstrap procedure replications. Default: num.bootstrap = 99.

width

a user-specified positive value (univariate conditional variable) or vector (multivariate conditional variable) for gaussian kernel bandwidth. Its default value is relies on stats::bw.nrd0 function when conditional variable is univariate, ks::Hpi.diag when conditional variable with at most trivariate, and stats::bw.nrd on the other cases.

distance

if distance = TRUE, x and y will be considered as distance matrices. Default: distance = FALSE.

index

exponent on Euclidean distance, in (0,2]

seed

the random seed

num.threads

number of threads. Default num.threads = 1.

Value

cdcov.test returns a list with class "htest" containing the following components:

statistic

conditional distance covariance statistic.

p.value

the p-value for the test.

replicates

the number of local bootstrap procedure replications.

size

sample sizes.

alternative

a character string describing the alternative hypothesis.

method

a character string indicating what type of test was performed.

data.name

description of data.

References

Wang, X., Pan, W., Hu, W., Tian, Y. and Zhang, H., 2015. Conditional distance correlation. Journal of the American Statistical Association, 110(512), pp.1726-1734.

See Also

cdcov

Examples

library(cdcsis)
set.seed(1)
num <- 50
################# Conditional Independent #################
## Case 1:
cov_mat <- matrix(c(1, 0.36, 0.6, 0.36, 1, 0.6, 0.6, 0.6, 1), nrow = 3)
dat <- mvtnorm::rmvnorm(n = num, sigma = cov_mat)
x <- dat[, 1]
y <- dat[, 2]
z <- dat[, 3]
cdcov.test(x, y, z)
## Case 2:
z <- rnorm(num)
x <- 0.5 * (z^3 / 7 + z / 2) + tanh(rnorm(num))
x <- x + x^3 / 3
y <- (z^3 + z) / 3 + rnorm(num)
y <- y + tanh(y / 3)
cdcov.test(x, y, z, num.bootstrap = 99)

################# Conditional Dependent #################
## Case 3:
cov_mat <- matrix(c(1, 0.7, 0.6, 0.7, 1, 0.6, 0.6, 0.6, 1), nrow = 3)
dat <- mvtnorm::rmvnorm(n = num, sigma = cov_mat)
x <- dat[, 1]
y <- dat[, 2]
z <- dat[, 3]
cdcov.test(x, y, z, width = 0.5)
## Case 4:
z <- matrix(rt(num * 4, df = 2), nrow = num)
x <- z
y <- cbind(sin(z[, 1]) + cos(z[, 2]) + (z[, 3])^2 + (z[, 4])^2, 
           (z[, 1])^2 + (z[, 2])^2 + z[, 3] + z[, 4])
z <- z[, 1:2]
cdcov.test(x, y, z, seed = 2)

################# Distance Matrix Input #################
x <- dist(x)
y <- dist(y)
cdcov.test(x, y, z, seed = 2, distance = TRUE)