Estimation of Penalized Spline Linear Regression Models through Robust M Estimator

Parametric regression approaches commonly used include simple linear, quadratic, and cubic linear regression. However, its use cannot be used for all data in the real case. Many data have data plots that do not follow parametric patterns, so we must use other approaches, including nonparametric regression. The spline is essentially a generalization of polynomial functions, where the optimization still adopts the concept in the parametric regression approach. The finalized spline regression curve is formed by minimizing the total residual subjects to the size of the spline coefficients. It seems that the least squared spline regression is notresistant to outliers.