论文标题
MLE在具有结构形状参数的两参数伽马混合模型下的一致性
Consistency of the MLE under a two-parameter gamma mixture model with a structural shape parameter
论文作者
论文摘要
有限的伽马混合模型通常用于描述收入数据，保险数据和其他应用程序数据中的随机性。但是，流行的可能性方法对于此模型不起作用，因为可能性函数是无限的，因此最大似然估计器的定义不当。已经进行了许多研究，以确保混合分布的一致估计，包括在形状参数上放置上限或对对数似然函数增加惩罚。在本文中，我们表明，如果有限γ混合模型中的形状参数是结构性的，那么混合分布的最大似然估计量是很好的定义且非常一致的。我们还提供了模拟结果，证明了估计量的一致性。我们说明了该模型使用结构规模参数的应用到家庭收入数据中。拟合的混合物分布从可支配收入的水平方面导致了几种可能的亚群结构。
The finite Gamma mixture model is often used to describe randomness in income data, insurance data, and data from other applications. The popular likelihood approach, however, does not work for this model because the likelihood function is unbounded, and the maximum likelihood estimator is therefore not well defined. There has been much research into ways to ensure the consistent estimation of the mixing distribution, including placing an upper bound on the shape parameter or adding a penalty to the log-likelihood function. In this paper, we show that if the shape parameter in the finite Gamma mixture model is structural, then the maximum likelihood estimator of the mixing distribution is well defined and strongly consistent. We also present simulation results demonstrating the consistency of the estimator. We illustrate the application of the model with a structural scale parameter to household income data. The fitted mixture distribution leads to several possible subpopulation structures in terms of the level of disposable income.
