论文标题
半参数贝叶斯概括的最小二乘估计器
A Semi-Parametric Bayesian Generalized Least Squares Estimator
论文作者
论文摘要
在本文中，我们提出了半参数贝叶斯广义的最小二乘估计器。在每个误差为矢量的通用设置中，参数概括的最小平方估计器维持这样的假设，即每个误差向量具有相同的分布参数。但是，实际上，错误在分布方面可能是异质的。为了应对这种异质性，引入了误解的差异过程，以实现误差的分布参数，导致错误分布是可变数量的正常分布的混合物。我们的方法使正常组件的数量是数据驱动的。然后介绍了两种特定情况的半参数贝叶斯估计器：方程系统看似无关的回归和面板数据的随机效应模型。我们设计了一系列仿真实验，以探索估计器的性能。结果表明，与贝叶斯估计器相比，使用正常分布或正态分布的参数混合物比贝叶斯估计器获得了较小的后标准偏差和平方误差。然后，我们将半参数贝叶斯估计器应用于方程系统和面板数据模型中。
In this paper we propose a semi-parametric Bayesian Generalized Least Squares estimator. In a generic setting where each error is a vector, the parametric Generalized Least Square estimator maintains the assumption that each error vector has the same distributional parameters. In reality, however, errors are likely to be heterogeneous regarding their distributions. To cope with such heterogeneity, a Dirichlet process prior is introduced for the distributional parameters of the errors, leading to the error distribution being a mixture of a variable number of normal distributions. Our method let the number of normal components be data driven. Semi-parametric Bayesian estimators for two specific cases are then presented: the Seemingly Unrelated Regression for equation systems and the Random Effects Model for panel data. We design a series of simulation experiments to explore the performance of our estimators. The results demonstrate that our estimators obtain smaller posterior standard deviations and mean squared errors than the Bayesian estimators using a parametric mixture of normal distributions or a normal distribution. We then apply our semi-parametric Bayesian estimators for equation systems and panel data models to empirical data.
