A Comparison of O'Sullivan Penalized Spline and Penalized Spline Based Truncated Power Basis Methods to Predict Ozone Concentrations

This paper aims to predict ozone concentrations based on the effects of ultraviolet light. Spline regression is piecewise polynomials that connect join points called knots. In spline regression, parameter estimation was fit by OLS (Ordinary Least Square) method. However, the OLS method leads to over parameterized and in the plot of estimated regression curve is fluctuated when using too much knots. Therefore, it needs an additional constraint which contains smoothing parameter, so that results an ideal fit. This parameter estimation method is known as PLS (Penalized Least Square) method. Spline regression using PLS method is called as penalized spline regression. O'Sullivan (1986) introduced a class of penalised splines based on B-spline basis functions. OPS (O'sullivan Penalized Spline) is a direct generalisation of smoothing splines that latter arises when the maximal number of B-spline basis functions included. One of the top performance measures the predicted regression curve that can be used is MSE (Mean Square Error). Results showed that the OPS method had a smaller MSE and GCV than the PSTPB (Penalized Spline Based Truncated Power Basis) method, so the use of the OPS method for predicting ozone against ultraviolet light was suitable to use.