Sparse estimations in kink regression model

When modeling the kink regression model, it is possible to have an excessive number of explanatory variables and their corresponding coefficients, thereby leading to the over-parameterization and multicollinearity problems. Motivated by these problems, five sparse estimation methods, namely LASSO, sparse Ridge, SCAD, MCP, and Bridge, are considered to perform simultaneous variable selection and parameter estimation, as alternatives to the Ordinary Least Squares (OLS), in the kink regression model. To compare the performance of these sparse estimators, both simulation and real data applications are proposed. According to the simulation results, we demonstrate the superior performance of sparse estimations in terms of selection accuracy and prediction by comparing them to the non-sparse estimations. However, it is not apparent which sparse estimations are more appropriate for estimating the kink regression. However, in an application study, the comparison result indicates that the SCAD penalty would be a preferable penalty function for the application of kink regression to the life expectancy data as the lowest EBIC and the highest \({\text{Adj - }}R^{2}\) are obtained.