论文标题
线性回归中贝叶斯推断的渐近特性随结构断裂
Asymptotic properties of Bayesian inference in linear regression with a structural break
论文作者
论文摘要
本文研究了贝叶斯方法的大型样本特性，以在结构断裂的线性回归模型中推断$γ$的推理。与没有考虑到未知休息位置$τ$的不确定性的常规推理方法相反，我们认为的贝叶斯方法融合了这种不确定性。我们的主要理论贡献是在广泛的先验中，$γ$的Bernstein-von Mises型定理（贝叶斯渐近正态性），这实际上表明传统的常见主义者和贝叶斯推论之间的渐近等效性。因此，一个常见的研究人员可以考虑$γ$的可信间隔，以检查$τ$的不确定性的鲁棒性。仿真研究表明，$γ$的常规置信区间倾向于在有限样本中卧底，而可靠的间隔通常提供了更合理的覆盖范围。随着样本量的增加，根据我们的理论结论所预测的两种方法一致。使用Paye和Timmermann（2006）对股票回报预测的数据，我们说明$γ$的传统置信区间可能不足以说明真正的采样不确定性。
This paper studies large sample properties of a Bayesian approach to inference about slope parameters $γ$ in linear regression models with a structural break. In contrast to the conventional approach to inference about $γ$ that does not take into account the uncertainty of the unknown break location $τ$, the Bayesian approach that we consider incorporates such uncertainty. Our main theoretical contribution is a Bernstein-von Mises type theorem (Bayesian asymptotic normality) for $γ$ under a wide class of priors, which essentially indicates an asymptotic equivalence between the conventional frequentist and Bayesian inference. Consequently, a frequentist researcher could look at credible intervals of $γ$ to check robustness with respect to the uncertainty of $τ$. Simulation studies show that the conventional confidence intervals of $γ$ tend to undercover in finite samples whereas the credible intervals offer more reasonable coverages in general. As the sample size increases, the two methods coincide, as predicted from our theoretical conclusion. Using data from Paye and Timmermann (2006) on stock return prediction, we illustrate that the traditional confidence intervals on $γ$ might underrepresent the true sampling uncertainty.
