论文标题
在两部分高斯混合模型下，最大似然估计的均匀收敛速率
Uniform Convergence Rates for Maximum Likelihood Estimation under Two-Component Gaussian Mixture Models
论文作者
论文摘要
我们得出了最大似然估计量的均匀收敛速率和最小值的下限，用于具有不平等方差的两个组件位置尺度高斯混合模型中的参数估计。我们假设混合物的混合比例是已知和固定的，但在下面的混合组件上没有分离假设。根据最佳参数估计率，相位转换显示为存在，具体取决于混合物是否平衡。我们分析的关键是对位置尺度高斯混合模型的参数之间的依赖性进行仔细研究，如多项式相等性的系统和不平等的系统所捕获的解决方案设置的范围驱动了我们获得的速率。一项模拟研究说明了这项工作的理论发现。
We derive uniform convergence rates for the maximum likelihood estimator and minimax lower bounds for parameter estimation in two-component location-scale Gaussian mixture models with unequal variances. We assume the mixing proportions of the mixture are known and fixed, but make no separation assumption on the underlying mixture components. A phase transition is shown to exist in the optimal parameter estimation rate, depending on whether or not the mixture is balanced. Key to our analysis is a careful study of the dependence between the parameters of location-scale Gaussian mixture models, as captured through systems of polynomial equalities and inequalities whose solution set drives the rates we obtain. A simulation study illustrates the theoretical findings of this work.
