Cubic spline data reduction choosing the knots from a third derivative criterion (Q5959241)

The authors present a data reduction method of functional data. In a first step a reference function \( f_\lambda \) is chosen which reflects the shape suggested by the data. The function \( f_\lambda \) is a natural cubic spline obtained by a variational principle which is governed by a smoothing parameter \(\lambda\). In a second step \( f_\lambda \) will be approximated by a cubic spline \(s_\lambda \) having a small numbers of knots. The choice of the knots depends on an iterative strategy by ``adding and moving a knot'' using a criterion based on the third derivative of \( f_\lambda .\) The authors illustrate their method by instructive numerical examples.