Cubic Spline Data Reduction, Choosing the Knots from a Third Derivative Criterion

This paper presents a data reduction method for functional data. Starting with noisy or not noisy data, we first define a function f , called the “reference function”, as a cubic smoothing spline which is supposed to have the global form of the data. This reference function is then used to locate the knots of the final approximating spline by using a criterion based on the third derivative of f . Then, the least-squares spline approximating all the data is derived with these knots. Numerical results show the effectiveness of the method.