compute_av {MCARtest}

Compute the columnwise average of means/variances

Description

A function that computes \bar{\operatorname{av}}_j(\mu_{\mathbb{S}}) as defined in Section 5 in Bordino and Berrett (2024), or \bar{\operatorname{av}}_j(\sigma^2_{\mathbb{S}}) as defined in Section 2 in Bordino and Berrett (2024). The sequence of means/variances, and the sequence of patterns, are calculated with getSigmaS.

Usage

compute_av(type, X)

Arguments

type

If set equal to "mean", computes \bar{\operatorname{av}}_j(\mu_{\mathbb{S}}). If set equal to "var", computes \bar{\operatorname{av}}_j(\sigma^2_{\mathbb{S}}).

X

The whole dataset with missing values.

Value

The value of \bar{\operatorname{av}}_j(\sigma^2_{\mathbb{S}}) or \bar{\operatorname{av}}_j(\mu_{\mathbb{S}}).

References

Bordino A, Berrett TB (2024). “Tests of Missing Completely At Random based on sample covariance matrices.” arXiv preprint 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)

xxx = get_SigmaS(X)$patterns
compute_av("var", X)
compute_av("mean", X)