The corrected χ2 test requires known kinship coefficients and inbreeding coefficients. We propose replacing these coefficients with their MLEs. We call this statistic a corrected χ2 test with estimated coefficients, Wχecorr2 and this is same as Wχcorr2 except that we use Φ̂ rather than the assigned Φ from a known pedigree structure. With estimates of kinship and inbreeding coefficients, unknown background relatedness or cryptic relatedness caused by common population history can be accommodated. An estimate of kinship would also be useful in the case that a sample includes a mixture of known and unknown relationships or any missing/misspecified pedigree relationships.
