Futschik Andreas, Gach Florian
Department of Statistics, University of Vienna, Austria.
Theor Popul Biol. 2008 Mar;73(2):212-21. doi: 10.1016/j.tpb.2007.11.009. Epub 2007 Dec 8.
We consider the estimation of the scaled mutation parameter theta, which is one of the parameters of key interest in population genetics. We provide a general result showing when estimators of theta can be improved using shrinkage when taking the mean squared error as the measure of performance. As a consequence, we show that Watterson's estimator is inadmissible, and propose an alternative shrinkage-based estimator that is easy to calculate and has a smaller mean squared error than Watterson's estimator for all possible parameter values 0<theta<infinity. This estimator is admissible in the class of all linear estimators. We then derive improved versions for other estimators of theta, including the MLE. We also investigate how an improvement can be obtained both when combining information from several independent loci and when explicitly taking into account recombination. A simulation study provides information about the amount of improvement achieved by our alternative estimators.
我们考虑对缩放后的突变参数θ进行估计，它是群体遗传学中关键的参数之一。我们给出了一个一般性结果，表明在以均方误差作为性能度量时，何时可以使用收缩法改进θ的估计量。结果表明，沃特森估计量是不可容许的，并提出了一种基于收缩的替代估计量，它易于计算，并且对于所有可能的参数值0 < θ < ∞，其均方误差都比沃特森估计量小。该估计量在所有线性估计量类中是可容许的。然后我们推导了θ的其他估计量（包括极大似然估计）的改进版本。我们还研究了在合并来自几个独立位点的信息以及明确考虑重组时，如何实现改进。一项模拟研究提供了有关我们的替代估计量所实现的改进量的信息。
