Variable Selection and Estimation in Kink Regression Model

Abstract

© 2020, The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG. Recently, regression kink model has gained an increasing popularity as it provides a richer information than the ordinary linear model in the light of an economic structural change. However, as the number of parameters in the kink regression model is larger than that of the linear version, the traditional least squares estimates are not valid and may provide infinite solutions, especially when the number of observations is small and there are many coefficients. To deal with this problem, the LASSO variable selection method is suggested to estimate the unknown parameters in the model. It not only provides the estimated coefficients, but also shrinks the magnitude of all the coefficients and removes some whose values have been shrunk to zero. This process helps decrease variance without increasing the bias of the parameter estimates. Thus, LASSO could play an important role in the kink regression model building process, as it improves the result accuracy by choosing an appropriate subset of regression predictors.