Eguchi S, Matsuura M
Department of Mathematics, Shimane University, Matsue, Japan.
Biometrics. 1990 Jun;46(2):415-26.
A new method of testing the Hardy-Weinberg equilibrium in the human leukocyte antigen (HLA) system is proposed and applied to real data. The derivation is based on the maximum likelihood method and closely related to standard regression theory. The test statistic has a closed representation of residual sum of squares by a projection mapping of data onto the estimated regression plane. Under the Hardy-Weinberg law the noniterative estimates for the gene frequencies are suggested by the use of the projection mapping. The test statistic and gene frequency estimates are shown to be asymptotically equivalent to the maximum likelihood method and to be more efficient than the other suggested test statistic when there are more than two identified alleles.
本文提出了一种检测人类白细胞抗原（HLA）系统中哈迪-温伯格平衡的新方法，并将其应用于实际数据。该方法的推导基于最大似然法，与标准回归理论密切相关。检验统计量通过将数据投影到估计的回归平面上，得到残差平方和的封闭表示。在哈迪-温伯格定律下，利用投影映射给出了基因频率的非迭代估计。当存在两个以上已识别的等位基因时，检验统计量和基因频率估计值与最大似然法渐近等价，且比其他建议的检验统计量更有效。
