ProjectionTest {MCARtest}

Carry out a test of MCAR in a contingency table, given incomplete observations.

Description

Carry out a test of MCAR in a contingency table, given incomplete observations.

Usage

ProjectionTest(pSh, nS, bS, M, B)

Arguments

pSh

A sequence of empirical mass functions calculated using incomplete observations.

nS

A sequence of integers giving the numbers of incomplete observations used to calculate pSh.

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.

B

An integer giving the number of bootstrap samples to be used to calibrate the test.

Value

The p-value the Monte Carlo test described in Berrett and Samworth (2023).

The value of the test statistic R().

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) # Our canonical 3d example
M=c(2,2,2)
nS=c(200,200,200)

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)
P12=pS[1:4]; P13=pS[5:8]; P23=pS[9:12]
X12=t(rmultinom(1,size=nS[1],prob=P12)/nS[1])
X13=t(rmultinom(1,size=nS[2],prob=P13)/nS[2])
X23=t(rmultinom(1,size=nS[3],prob=P23)/nS[3])
pSh=cbind(X12,X13,X23)

ProjectionTest(pSh,nS,bS,M,99)