av: Compute the columnwise average of a collection of vectors.

In MCARtest: Optimal Nonparametric Testing of Missing Completely at Random

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 \insertCiteBB2024;textualMCARtest.

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

\insertRef

BB2024MCARtest

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)

MCARtest documentation built on June 26, 2025, 5:08 p.m.