ABSTRACT
Splines form an important class of functions in non-parametric regression problems where the regression model needs to be flexible while satisfying a smoothness condition. Spline based models also allow some useful constraints to be imposed in addition to smoothness. Splines are more commonly referred to in terms of the degree of the polynomial pieces rather than their order. The basic concept of a spline can be generalized to data where there are multiple identical breakpoints. For the case of cubic splines, where there are two extra conditions, some of the popular choices are as follows: Natural spline, Clamped spline, Periodic spline, Not-a-knot spline. The recursions start with B-splines of order 1, which are piecewise constant functions, and build up B-splines of a higher order using the ones from the previous order.
