Rindex {MCARtest}

A function computing the incompatibility index

Description

A function solving a linear program to compute the incompatibility index R() defined in Berrett and Samworth (2023), in the case of having discrete random variables. Uses Amatrix to define to constraint matrix and lpSolve to implement the linear optimisation.

Usage

Rindex(pS, bS, M)

Arguments

pS

A sequence of probability mass functions on the marginal spaces.

bS

A binary matrix specifying the set of observation patterns. Each row encodes a single pattern.

M

A vector of positive integers giving the alphabet sizes of the discrete variables.

Value

The value of R(), in the interval [0,1].

References

Berrett TB, Samworth RJ (2023). “Optimal nonparametric testing of Missing Completely At Random, and its connections to compatibility.” Ann. Statist., 51, 2170–2193.

Examples

bS=matrix(c(1,1,0, 1,0,1, 0,1,1),byrow=TRUE,ncol=3)
M=c(2,2,2)

pS=rep(0.25,12)
Rindex(pS,bS,M)

pS=c(0.125,0.375,0.375,0.125,0.250,0.250,0.250,0.250,0.100,0.400,0.400,0.100)
Rindex(pS,bS,M)