Asymptotic properties of Bayesian inference in linear regression with a structural break
研究了线性回归模型存在结构突变时，贝叶斯方法对斜率参数的渐近性质，证明其与频率学派推断渐近等价，并通过模拟和实例说明贝叶斯可信区间在小样本下覆盖更合理。
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 date, 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 the break date. 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.