Statistical Estimation in Piecewise Linear Regression Models

The kink regression model assumes that linear regression forms are separately modelled on two sides of an unknown threshold but still continuous at the threshold. This paper considers statistical estimation for piecewise linear regression models which are widely used in various fields to capture nonlinear relationships between variables. The estimators for the kink locations and regression coefficients are obtained by using the least squares method, a detailed explanation of the estimation process is provided. Furthermore, the proposed methodology is validated through an illustrative example using Monte Carlo random simulation, demonstrating its effectiveness in accurately capturing nonlinear patterns and changes in the data.