Estimation and Inference for Multi-Kink Quantile Regression
提出多拐点分位数回归模型，用迭代分段分位数回归算法估计系数和拐点位置，理论证明拐点数选择一致性和估计渐近正态性，并开发R包，适用于中国产业结构等数据分析。
This article proposes a new Multi-Kink Quantile Regression (MKQR) model which assumes different linear quantile regression forms in different regions of the domain of the threshold covariate but are still continuous at kink points. First, we investigate parameter estimation, kink points detection and statistical inference in MKQR models. We propose an iterative segmented quantile regression algorithm for estimating both the regression coefficients and the locations of kink points. The proposed algorithm is much more computationally efficient than the grid search algorithm and not sensitive to the selection of initial values. Second, asymptotic properties, such as selection consistency of the number of kink points and asymptotic normality of the estimators of both regression coefficients and kink effects, are established to justify the proposed method theoretically. Third, a score test based on partial subgradients is developed to verify whether the kink effects exist or not. Test-inversion confidence intervals for kink location parameters are also constructed. Monte Carlo simulations and two real data applications on the secondary industrial structure of China and the triceps skinfold thickness of Gambian females illustrate the excellent finite sample performances of the proposed MKQR model. A new R package MultiKink is developed to easily implement the proposed methods.