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This paper discusses the estimation problem of recombination fractions under some natural inequality restrictions in phase-unknown triple backcross population. We consider the offspring phenotype classification of multiple offspring family, and present an explicit formula of the number of the offspring phenotype classification. We then adopt the restricted expectation-maximization (REM) algorithm to estimate the two-locus recombination fractions based on the data of phenotype classification. Simulation studies show that the REM algorithm outperforms unrestricted method, and validate that family with more offspring can provide more linkage information.本文针对相型信息未知的三回交家系讨论了在自然的序约束下重组率的估计问题. 考虑了多后代数据的后代表型分类问题, 给出了后代表型分类数的一个具体公式. 基于表型分类所得数据采用约束EM 算法(REM) 估计了两位点重组率. 鉴于交换干扰的存在可能会影响到基因定位的精度, 基于该估计, 进一步考虑了有关生物体基因组中交换干扰的统计推断问题. 实例和模拟研究均显示REM算法要优于无约束算法, 并证实了多后代家庭会提供更多连锁信息这一观点

约束下多子女家系数据重组率的最大似然估计