Berwin Turlach, Department of Statistics and Applied Probability, National University of Singapore

Monotone penalised spline smoothing

Abstract:

Penalised spline smoothing (Eilers and Marx, 1996; Ruppert and
Carroll, 2000) is, arguably, fast becoming the method of choice for
non- and semiparametric regression models.  The attractiveness of
penalised spline smoothers is twofold.  First, compared with other
smoothing methods, e.g. smoothing splines or kernel smoother, fitting
penalised splines smoothers is computationally less complex.
Secondly, the connection between smoothing methods and mixed models
(Speed, 1991) is particularly easy to establish for penalised spline
smoothers.  Thus, it is easy to incorporate a penalised spline
smoother into a semiparametric regression model and fit the model
using standard software available for fitting (linear) mixed models
(Ruppert, Wand and Carroll, 2003).

However, in some situations, one would like to combine the flexibility
of nonparametric smoothing techniques with prior knowledge in the form
of constraints on the response curve given by, say, a physical or
economic theory.  In this talk, we discuss how monotonicity
constraints can be imposed on penalised spline smoothers.