A Continuous Piecewise Expectile Regression With Multiple Change-points And Its Application

In big data era,the threshold effect data exists in various fields such as finance,economics,psychology,biology and computer science.The regression analysis method usually used for threshold data is to use threshold least-squares regression.However,the least-squares regression,which is based on the data of mean,can only describe the mean of the response.In contrast,the quantile regression model can describe the full figures of the data.However,there are more crossing between quantile curves.Expectile regression can not only get the full picture of data,but also it is not easy to cross the fitting line.Although the quantile regression is more robust,the expectile regression has advantages in computational convenience,estimation of validity,and simplicity of estimating the conditional density function.Therefore,it is of great theoretical and practical meanings to study the multiple continuous threshold Expectile regression model.In this paper,we study the multiple continuous threshold expectile regression model.Firstly,since the objective function is not differentable at the threshold locations,the estimation is very difficult.To solve this problem,we use a kernel function to approximate the objective function at the threshold.Secondly,the number of thresholds of the model is not prior known,it requires a data-driven estimate for the number of thresholds.We propose the variable selection method,SCAD,to determine the number of thresholds and to estimate the model coefficients.Finally,the estimated parameters of the model are used to obtain the exact parameters of the model.Numerical simulations are investigated the finite-sample performance of our method.We also use the multiple continuous threshold expectile regression model to three applications,including the relationship between salary and service age of baseball pitchers,GDP and government debt rates,body mass index(BMI)and age.