Estimation and inference for multikink expectile regression with longitudinal data

In this article, we investigate parameter estimation, kink points testing and statistical inference for a longitudinal multikink expectile regression model. The estimators for the kink locations and regression coefficients are obtained by using a bootstrap restarting iterative algorithm to avoid local minima. A backward selection procedure based on a modified BIC is applied to estimate the number of kink points. We theoretically demonstrate the number selection consistency of kink points and the asymptotic normality of all estimators. In particular, the estimators of kink locations are shown to achieve root-n consistency. A weighted cumulative sum type statistic is proposed to test the existence of kink effects at a given expectile, and its limiting distributions are derived under both the null and the local alternative hypotheses. The traditional Wald-type and cluster bootstrap confidence intervals for kink locations are also constructed. Simulation studies show that the proposed estimators and test have desirable finite sample performance in both homoscedastic and heteroscedastic errors. Two applications to the Nation Growth, Lung and Health Study and Capital Bike sharing dataset in Washington D.C. are also presented. The R codes for simulation studies and the real data are available at https://github.com/wangleink/MKER.