Under the classical long-span asymptotic framework, we develop a class of generalized laplace (GL) inference methods for the change-point dates in a linear time series regression model with multiple structural changes analyzed in, e.g., Bai and Perron (1998, Econometrica 66, 47–78). The GL estimator is defined by an integration rather than optimization-based method and relies on the LS criterion function. It is interpreted as a classical (non-Bayesian) estimator, and the inference methods proposed retain a frequentist interpretation. This approach provides a better approximation about the uncertainty in the data of the change-points relative to existing methods. On the theoretical side, depending on some input (smoothing) parameter, the class of GL estimators exhibits a dual limiting distribution, namely the classical shrinkage asymptotic distribution or a Bayes-type asymptotic distribution. We propose an inference method based on highest density regions using the latter distribution. We show that it has attractive theoretical properties not shared by the other popular alternatives, i.e., it is bet-proof. Simulations confirm that these theoretical properties translate to good finite-sample performance.

中文翻译：

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多变点模型中的广义拉普拉斯推理

在经典的大跨度渐近框架下，我们开发了一类广义拉普拉斯（GL）推理方法，用于线性时间序列回归模型中的变化点日期，其中分析了多个结构变化，例如 Bai 和 Perron（1998，计量经济学66, 47–78)。GL 估计器是通过集成而不是基于优化的方法定义的，并且依赖于 LS 准则函数。它被解释为经典（非贝叶斯）估计量，并且提出的推理方法保留了常客解释。相对于现有方法，这种方法提供了关于变化点数据不确定性的更好近似。在理论方面，根据某些输入（平滑）参数，GL 估计器类表现出双重限制分布，即经典收缩渐近分布或贝叶斯型渐近分布。我们提出了一种基于使用后一种分布的最高密度区域的推理方法。我们表明它具有其他流行的替代方案所不具备的有吸引力的理论特性，即它是可赌的。