Estimation of gene frequency and test for Hardy-Weinberg equilibrium in the HLA system

This paper concerns the testing for Hardy-Weinberg equilibrium and the estimation of gene frequency in the human leukocyte antigens (HLA) system. An extensive simulation study for both testing and estimation is given for investigating the performance of the projection method by Eguchi and Matsuura, which has a closed form, and the method is asymptotically equivalent to the maximum likelihood method. We compare our projection test statistic with the likelihood ratio test and the single degree of freedom chi-square test suggested by Nam and Gart. Actual mean square errors of the projection estimator of gene frequency under the Hardy-Weinberg equilibrium are compared with the maximum likelihood estimator and some other estimators recently discussed by Nam.