Comparison of Significant Approaches of Penalized Spline Regression (P-splines)

Over the last two decades P-Splines have become a popular modeling tool in a wide class of statistical contexts. Fundamentally, semiparametric regression methods combine the leads of parametric and nonparametric approaches to regression analysis, while in precise, penalized spline regression uses the knowledge of nonparametric spline smoothing as a generalization of smoothing splines that let more suppleness in a choice of model with respect to the basis functions and the penalty. The present article compares two significant approaches of penalized spline regression models named as p-splines based on different basis functions with numerous knot selections and various types of penalties. These model fits have been applied on Wood Strength data to compare by calculating nonlinear least square method; also approaches are compared on several aspects: numerical immovability, quality of fit, derivative estimation and smoothing. This comparison will help us to fit best suitable model for conforming best suitable conditions and scenarios.