| 讲座简介： | This paper considers a multiple threshold regression model, where the coefficient parameters can switch between regimes according to the value of a threshold variable, and establishes the valid inference of a Lasso-type shrinkage estimation procedure that consistently estimates the multiple thresholds. The procedure is robust to both diverging number of thresholds and shrinking threshold effects. Asymptotic properties, including the consistency of the group Lasso estimators and threshold number estimator, and limiting distribution of the threshold estimators and the likelihood ratio statistic, are established under a set of regularity conditions. The focus is further placed on the new development of the post-Lasso inferential theory, which accounts for the randomness of threshold selection and is achieved by characterizing the distribution of the coefficient estimators conditional on the selected model. Monte Carlo simulations demonstrate that the estimators are well-behaved in finite samples. An empirical application to return prediction further illustrates the practical merits of our methodology. |
