GENERALIZED LAPLACE INFERENCE IN MULTIPLE CHANGE-POINTS MODELS
针对线性时间序列回归模型中的多个结构变化点，提出一类基于积分而非优化的广义拉普拉斯估计量，提供更好的不确定性近似，并具有双重极限分布和防篡改的理论性质。
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.