The Statistical Inference Of Generalized Linear Model With Covariate Threshold Effects

Change point refers to the structure or distribution where the research model changes systematically.It is widely used in sociology,bio-medicine,pharmacy,climatology,econometrics,risk management and industrial production.The model is heterogeneous when change point occurs,ignoring the change point will lead to a wrong conclusion,therefore the estimation of the structural mutation model is very important.It is worth noting that although much work has been done on the structural mutation model,there is still little research on the change point under the generalized linear model.Therefore,this paper considers the statistical inference of generalized linear model with covariate threshold effect.We use the maximum likelihood and the smoothing method to overcome the theoretical derivation and computational difficulty caused by the explicit function,so as to estimate the proposed model.We prove the asymptotic properties of the estimated parameters under the classical framework,and obtain the consistency and asymptotic normality of the parameters of interest.In addition,numerical simulation is carried out under the framework of logistic regression and poisson regression respectively,and the performance of the proposed method in limited samples is evaluated.Finally,the model is applied to the analysis of happiness data,and a series of interesting conclusions are obtained.