论文标题
关于参数估计的两阶段方法的统计决策理论观点
A Statistical Decision-Theoretical Perspective on the Two-Stage Approach to Parameter Estimation
论文作者
论文摘要
系统识别和统计中最重要的问题之一是如何估计给定模型的未知参数。在可以计算可能性函数的情况下，可以使用优化方法和专业程序，例如经验最小化（EM）。对于只能从参数模型中模拟但难以评估的可能性或无法评估的可能性，可以应用一种称为两阶段（TS）方法的技术来获得可靠的参数估计。不幸的是，目前缺乏TS理论理由。在本文中，我们提出了TS的统计决策理论推导，这导致了贝叶斯和微型估计器。我们还展示了如何通过将数据的分位数计算为第一步，并将线性函数用作第二阶段，将TS方法应用于模型上的模型。通过数值模拟说明了所提出的方法。
One of the most important problems in system identification and statistics is how to estimate the unknown parameters of a given model. Optimization methods and specialized procedures, such as Empirical Minimization (EM) can be used in case the likelihood function can be computed. For situations where one can only simulate from a parametric model, but the likelihood is difficult or impossible to evaluate, a technique known as the Two-Stage (TS) Approach can be applied to obtain reliable parametric estimates. Unfortunately, there is currently a lack of theoretical justification for TS. In this paper, we propose a statistical decision-theoretical derivation of TS, which leads to Bayesian and Minimax estimators. We also show how to apply the TS approach on models for independent and identically distributed samples, by computing quantiles of the data as a first step, and using a linear function as the second stage. The proposed method is illustrated via numerical simulations.
