A Generalized Maximum Renyi Entropy Approach in Kink Regression Model

Abstract

This study aims to estimate the kink regression model with the small sample size since the small sample size will lead to an undetermined or ill-posed problem. Thus, to solve these problems, the generalized maximum entropy (GME), based Renyi measure is proposed. Specifically, we replace the Shannon entropy with Renyi entropy to GME estimator. Monte Carlo simulation and the real data are used to evaluate the performance of Renyi GME estimator in Kink regression model. The results demonstrate that Renyi measure does not perform better than Shannon measure when the error is assumed to be normal. However, it is comparable to the Shannon entropy when the errors are assumed to be uniform, chi-square, and Student-t distributions. We then conduct two application studies to validate the performance of the Renyi GME and similar performance is obtained. Thus, we increase the number of order α to be larger than 2 and the result indicates that our high-order Renyi GME is clearly better than the traditional Shannon GME.