Estimation And Inference For Longitudinal Multi-Kink Regression With Exponential Squared Loss

Kink regression model describes the relationship between response variables and covariates,which is widely used in finance,economy,industry,medicine and other fields.In this dissertation,we investigate robust parameter estimation and statistical inference for a longitudinal multi-kink regression model.Due to the non-differentiable loss function caused by kink effects,a local linear smoothing technique is applied to deal with the original multi-kink regression model.Then,generalized estimation equations are constructed for the smooth-adjusted model,and a parameter estimation algorithm based on Newton-Raphson iterative algorithm is proposed using the modified Cholesky decomposition method.Besides,it is worth noting that the tuning parameter in the exponential square loss function has a significant effect on the estimation process.In order to achieve the robust estimation of parameters,an adaptive selection algorithm for the tuning parameter is provided.Furthermore,a weighted cumulative sum type statistic for verifying the existence of kink effects and a Bayesian information criteria for determining the number of kink points are developed.In addition,the asymptotic properties are established under some mild conditions.Finally,numerical simulation studies and the application in the progesterone data show the finite sample performance of the proposed methods.