Simple test for the Hardy-Weinberg law for HLA data with no observed double blanks

Eguchi and Matsuura (1990, Biometrics 46, 415-426) noted that the generalized Stevens test statistic for the Hardy-Weinberg law for human leukocyte antigen (HLA) data yields an excessively large value when no double blanks are observed. In this paper, we investigated this aberrant case. The inflated value of the test statistic is caused mainly by a seriously biased Bernstein's estimator of the recessive. We propose the generalized Stevens test using bias-corrected Bernstein's estimators for HLA data with no observed double blanks. An example illustrates the correction of the test statistic.