Comparison of simple and modified Bernstein's methods in estimation of recessive allele frequency in the HLA system

Bias and inefficiency of Bernstein's estimator of the recessive allele frequency in generalized ABO-like systems are important for situations where the frequency is small and the number of codominant alleles is large. A modified Bernstein's estimator of the recessive (Smith, 1967) has much smaller bias and higher efficiency than Bernstein's for large samples. Analogous findings are generally observed for small and moderate samples by Monte Carlo experiments. The modified method is preferred for the recessive frequency in the HLA system. The results are illustrated by numerical examples.