jdcov.stat: Joint distance covariance
In shubhadeep4/jdcov: Tests for joint independence via joint distance covariance

Description Usage Arguments Value References Examples

Computes the joint distance covariance (JdCov) among d(>=2) random vectors X_1, .. , X_d of (arbitrary) dimensions p_1, .. , p_d, defined in Section 2.2 in Chakraborty and Zhang (2019). The population JdCov among X_1, .. , X_d is zero if and only if the random vectors are jointly independent.

1	jdcov.stat(x, cc = 1, stat.type = "U")

`x`	a list of d (>=2) elements, the i^th element being a numeric n*p_i data matrix for the random vector X_i, i = 1,..,d. n denotes the sample size and p_i denotes the dimension of the i^th random vector X_i.
`cc`	a numeric value specifying the choice of the tuning parameter c, default is 1.
`stat.type`	a character string specifying the type of the estimator of joint distance covariance to be computed. The available options are : "V" (the V-statistic type estimator), "U" (the U-statistic type estimator), "US" (the scale invariant U-statistic type estimator), "Rank V" (the rank based V-statistic type estimator) and "Rank U" (the rank based U-statistic type estimator). Default is "U".

Returns the observed value of the squared sample joint distance covariance depending on the type of the estimator specified.

Chakraborty, S. and Zhang, X. (2019). Distance Metrics for Measuring Joint Dependence with Application to Causal Inference, Journal of the American Statistical Association, DOI: 10.1080/01621459.2018.1513364.

## (X_1, .. , X_d) are generated as follows : X=Z^3, where
## Z~N(0,diag(d)).

library(mvtnorm)
n=100; d=5
set.seed(10)
z=rmvnorm(n,mean=rep(0,d),sigma=diag(d)) ; x=z^3
X <- lapply(seq_len(ncol(x)), function(i) as.matrix(x[,i]))
jdcov.stat(X, cc=1, stat.type = "U")


## X, Y and Z are p-dimensional random vectors, where X, Y  
## are i.i.d N(0, diag(p)), Z_1 = sign(X_1 * Y_1) * W and 
## Z_{2:p} ~ N(0, diag(p-1)), W ~ exponential(mean=sqrt(2)). 

library(mvtnorm)
n=100 ; d=3; p=5
x=list() ; x[[1]]=x[[2]]=x[[3]]=matrix(0,n,p)
set.seed(1)
x[[1]]=rmvnorm(n,rep(0,p),diag(p)) 
set.seed(2)
x[[2]]=rmvnorm(n,rep(0,p),diag(p))
set.seed(3)
W=rexp(n,1/sqrt(2))
x[[3]][,1]=(sign(x[[1]][,1] * x[[2]][,1])) * W
set.seed(4)
x[[3]][,2:p]=rmvnorm(n,rep(0,(p-1)),diag(p-1))
jdcov.stat(x, cc=1, stat.type = "US")