av {MCARtest} | R Documentation |
Compute the columnwise average of a collection of vectors.
Description
A function that computes |\mathbb{S}_j|^{-1} \sum_{S \in \mathbb{S}_j} x_{S,j}
for a collection of vectors x_{\mathbb{S}}
over the missingness patterns.
This is defined in Step 3 of Algorithms 2 and 3 in Bordino and Berrett (2025).
Usage
av(x_S, patterns)
Arguments
x_S |
The collection of vectors over missingness patterns. |
patterns |
The collection of missingness patterns. |
Value
The vector of entry |\mathbb{S}_j|^{-1} \sum_{S \in \mathbb{S}_j} x_{S,j}
.
References
Bordino A, Berrett TB (2025). “Tests of Missing Completely At Random based on sample covariance matrices.” Ann. Statist., to appear, arXiv:2401.05256.
Examples
library(MASS)
d = 3
n = 200
SigmaS=list() #Random 2x2 correlation matrices (necessarily consistent)
for(j in 1:d){
x=runif(2,min=-1,max=1); y=runif(2,min=-1,max=1); SigmaS[[j]]=cov2cor(x%*%t(x) + y%*%t(y))
}
X = data.frame(matrix(nrow = 3*n, ncol = 3))
X[1:n, c(1,2)] = mvrnorm(n, c(0,0), SigmaS[[1]])
X[(n+1):(2*n), c(2, 3)] = mvrnorm(n, c(0,0), SigmaS[[2]])
X[(2*n+1):(3*n), c(1, 3)] = mvrnorm(n, c(0,0), SigmaS[[3]])
X = as.matrix(X)
tmp = get_SigmaS(X)
av(tmp$mu_S, tmp$patterns)
[Package MCARtest version 1.3 Index]