get_SigmaS {MCARtest}

Computes the sequence of patterns, means, variances, covariance and correlation matrices for a given dataset with missing values.

Description

Using the same the notation of Bordino and Berrett (2024), computes the sequence of patterns \mathbb{S}, means \mu_\mathbb{S}, variances \sigma^2_\mathbb{S}, and correlation matrices \Sigma_\mathbb{S} for a dataset with missing values.

Usage

get_SigmaS(X)

Arguments

X

The dataset with incomplete data.

Value

patterns The sequence of patterns \mathbb{S}.

n_pattern The cardinality of \mathbb{S}.

data_pattern A vector where the data are grouped according to \mathbb{S}.

muS The sequence of means.

C_S The sequence of covariance matrices.

sigma_squared_S The sequence of variances.

SigmaS The sequence of correlation matrices.

ambient_dimension The dimension d of the data.

References

Bordino A, Berrett TB (2024). “Tests of Missing Completely At Random based on sample covariance matrices.” arXiv preprint arXiv:2401.05256.

Examples

library(copula)
library(missMethods)
library(misty)
n = 1000

cp = claytonCopula(param = c(1), dim = 5)
P = mvdc(copula = cp, margins = c("exp", "exp", "exp", "exp", "exp"),
         paramMargins = list(list(1), list(1), list(1), list(1), list(1)))
X = rMvdc(n, P)
X = delete_MCAR(X, 0.1, c(1,4,5))

get_SigmaS(X)