M {MCARtest}R Documentation

Computes an inconsistency index for a collection of means.

Description

A function that computes the inconsistency index M(\mu_\mathbb{S}) for a collection of means, as defined in Algorithm 2 in Section 6 of Bordino and Berrett (2025).

Usage

M(mu_S, patterns)

Arguments

mu_S

A list of means \mu_\mathbb{S}.

patterns

A list of missingness patterns.

Value

The value of M().

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)
M(tmp$mu_S, tmp$patterns)

[Package MCARtest version 1.3 Index]