Semiparametric Inference in a Genetic Mixture Model
遗传混合模型中的半参数推断AI 解读 ↓
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遗传混合模型中的半参数推断
- 研究问题
- 在混合比例已知、成分分布可能误设且窝内个体数随机的遗传研究中，如何估计混合模型并检验两个成分是否相同？
- 方法与思路
- 作者在指数倾斜假设下构造经验似然，借助高阶展开处理零假设下退化的信息矩阵，并使用EM算法求半参数似然估计。
- 材料陈述的贡献
- 摘要称，论文得到参数估计的非标准收敛速度与经验似然比的极限分布，亦可估计成分分布，并报告模拟和癌症应用表现。
- 阅读关注点
- 应核对指数倾斜限制、随机簇大小与窝内依赖的处理、信息退化下高阶展开的条件，以及与参数方法比较的设定。
- 阅读边界
- 仅依据稿件版本未注明的索引摘要；完整正则条件、极限分布及比较数值未提供，摘要所称表现更好不能视为普遍优越性。
原文摘要
In genetic backcross studies, data are often collected from complex mixtures of distributions with known mixing proportions. Previous approaches to the inference of these genetic mixture models involve parameterizing the component distributions. However, model misspecification of any form is expected to have detrimental effects. We propose a semiparametric likelihood method for genetic mixture models: the empirical likelihood under the exponential tilting model assumption, in which the log ratio of the probability (density) functions from the components is linear in the observations. An application to mice cancer genetics involves random numbers of offspring within a litter. In other words, the cluster size is a random variable. We wish to test the null hypothesis that there is no difference between the two components in the mixture model, but unfortunately we find that the Fisher information is degenerate. As a consequence, the conventional two-term expansion in the likelihood ratio statistic does not work. By using a higher-order expansion, we are able to establish a nonstandard convergence rate N− 1/4 for the odds ratio parameter estimator β^. Moreover, the limiting distribution of the empirical likelihood ratio statistic is derived. The underlying distribution function of each component can also be estimated semiparametrically. Analogously to the full parametric approach, we develop an expectation and maximization algorithm for finding the semiparametric maximum likelihood estimator. Simulation results and a real cancer application indicate that the proposed semiparametric method works much better than parametric methods. Supplementary materials for this article are available online.