Entropy inference in smooth transition kink regression

Abstract

This study proposes a smooth transition kink regression model to capture the nonlinear relationship between dependent and independent variables. Our model generalizes that considered in Hansen to allow the continuous regression to be smoothed at any threshold or kink points. We allow the kink effects to be different for all relationships between each independent variable and the dependent variable. Also, in some cases, the regression typed model may have ill-posed problems (if the number of unknown parameters exceeds the number of observations or the underlying distribution is unknown). Therefore, Generalized Maximum Entropy (GME) estimation is applied for estimating our model. This study conducts experiments based on both simulation and real dataset, with comparison to multiple traditional estimations, including the standard Least Squares, Bayesian, and Maximum Likelihood. Experimental results show that the GME estimation is a useful tool for parameter estimates. Simulations also reveal excellent finite sample properties of the suggested method of estimation where the data is limited, and non-normal distribution is held.

Keywords:

• Generalized maximum entropy
• Kink regression
• Smooth transition function

Acknowledgments

The authors would like to thank all the reviewers for their helpful comments and suggestions to improve this paper. The authors are also grateful for the financial support offered by the Center of Excellence in Econometrics, Chiang Mai University, Thailand.