Flexible smoothing with P-splines: a unified approach

We consider the application of P-splines (Eilers and Marx, 1996) to three classes of models with smooth components: semiparametric models, models with serially correlated errors, and models with heteroscedastic errors. We show that P-splines provide a common approach to these problems. We set out a simple nonparametric strategy for the choice of the P-spline parameters (the number of knots, the degree of the P-spline, and the order of the penalty) and use mixed model (REML) methods for smoothing parameter selection. We give an example of a model in each of the three classes and analyse appropriate data sets.