论文标题
非中性Wright-Fisher扩散中选择的似然比和估计量的收敛性
Convergence of Likelihood Ratios and Estimators for Selection in non-neutral Wright-Fisher Diffusions
论文作者
论文摘要
许多离散时间，遗传学中描述等位基因频率动力学的有限种群大小模型已知会融合（可根据适当的缩放比例）与无限种群限制的扩散过程相聚，称为Wright-fisher扩散。在本文中，我们表明，在选择和突变参数中，扩散是偶然的，并且通过对随机微分方程的解决方案所诱导的度量在局部渐近正常上是统一的。随后，这两个结果用于分析选择和突变对种群作用时，最大可能性和贝叶斯估计量的统计特性。特别是，这表明这些估计器在紧凑的集合一致性上均匀地均匀，在紧凑型集合上的选择参数渐近差异和矩的收敛性中显示均匀，并且对于适当的损失函数而言渐近效率。
A number of discrete time, finite population size models in genetics describing the dynamics of allele frequencies are known to converge (subject to suitable scaling) to a diffusion process in the infinite population limit, termed the Wright-Fisher diffusion. In this article we show that the diffusion is ergodic uniformly in the selection and mutation parameters, and that the measures induced by the solution to the stochastic differential equation are uniformly locally asymptotically normal. Subsequently these two results are used to analyse the statistical properties of the Maximum Likelihood and Bayesian estimators for the selection parameter, when both selection and mutation are acting on the population. In particular, it is shown that these estimators are uniformly over compact sets consistent, display uniform in the selection parameter asymptotic normality and convergence of moments over compact sets, and are asymptotically efficient for a suitable class of loss functions.
