On the asymptotic behavior of the estimate of the recombination fraction under the null hypothesis of no linkage when the model is misspecified

We show that under the null hypothesis of no linkage the maximum likelihood estimator of the recombination fraction converges to 1/2 even when the trait-related parameter values in the likelihood function are misspecified. Furthermore, we show that under the null hypothesis of no linkage, but with misspecified trait-related parameter values, the negative of twice the natural logarithm of the likelihood ratio statistic still has a limiting chi-square distribution with 1 degree of freedom.