Kink model is developed to analyze the data where the regression function is two-stage piecewise linear with respect to the threshold covariate but continuous at an unknown kink point.In quantile regression for longit...Kink model is developed to analyze the data where the regression function is two-stage piecewise linear with respect to the threshold covariate but continuous at an unknown kink point.In quantile regression for longitudinal data,kink point where the kink effect happens is often assumed to be heterogeneous across different quantiles.However,the kink point tends to be the same across different quantiles,especially in a region of neighboring quantile levels.Incorporating such homogeneity information could increase the estimation efficiency of the common kink point.In this paper,we propose a composite quantile estimation approach for the common kink point by combining information from multiple neighboring quantiles.Asymptotic normality of the proposed estimator is studied.In addition,we also develop a sup-likelihood-ratio test to check the existence of the kink effect at a given quantile level.A test-inversion confidence interval for the common kink point is also developed based on the quantile rank score test.The simulation studies show that the proposed composite kink estimator is more efficient than the single quantile regression estimator.We also illustrate the proposed method via an application to a longitudinal data set on blood pressure and body mass index.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.11922117,11771361)Fujian Provincial Science Fund for Distinguished Young Scholars(Grant No.2019J06004)。
文摘Kink model is developed to analyze the data where the regression function is two-stage piecewise linear with respect to the threshold covariate but continuous at an unknown kink point.In quantile regression for longitudinal data,kink point where the kink effect happens is often assumed to be heterogeneous across different quantiles.However,the kink point tends to be the same across different quantiles,especially in a region of neighboring quantile levels.Incorporating such homogeneity information could increase the estimation efficiency of the common kink point.In this paper,we propose a composite quantile estimation approach for the common kink point by combining information from multiple neighboring quantiles.Asymptotic normality of the proposed estimator is studied.In addition,we also develop a sup-likelihood-ratio test to check the existence of the kink effect at a given quantile level.A test-inversion confidence interval for the common kink point is also developed based on the quantile rank score test.The simulation studies show that the proposed composite kink estimator is more efficient than the single quantile regression estimator.We also illustrate the proposed method via an application to a longitudinal data set on blood pressure and body mass index.
