Bernstein's and gene-counting methods in generalized ABO-like systems

Although the simple and adjusted Bernstein's methods are fully efficient for m=2 and m=3 (ABO system) respectively, their efficiency declines for larger values of m. For m greater than or equal to 4, the adjusted or modified Bernstein's method with a single counting iteration leads to a nearly efficient estimator. A single degree of freedom chi-square test of the Hardy-Weinberg law for all m is derived. Some findings on the statistical efficiency of typing various numbers of antigens are given. All the results are illustrated in numerical examples.