Assessing the Quality of the Natural Cubic Spline Approximation

Abstract

In large samples, central limit and saddle-point approximation theory suggest that spline functions having just two or three knots may be used to approximate the log- likelihood function for a single parameter, with the approximating polynomial being quadratic inside and linear outside of the knots. Natural cubic splines, which are piecewise cubic inside of the extreme knots and linear outside of these knots, are frequently used in non-parametric regression and data mining. These two facts suggest the use of natural cubic splines to approximate the log-likelihood functions. In this study we will show how to evaluate quality of those approximation by the monte carlo simution.