Student Prize Award

Abstract

P-splines regression is a flexible smoothing tool in which the starting point is a highly parameterised model and overfitting is prevented by introducing a penalty function. A common form of the penalty term is obtained by taking a prespecified order of differences of adjacent coefficients. This paper deals with a data-driven choice of the differencing order, as such allowing for the fit to adapt automatically to the (unknown) degree of smoothness of the underlying function. The selection procedure is based on Akaike's information criterion. The study is carried out in a broad framework of generalised linear and generalised additive models. We provide the necessary theoretical support for the selection procedure, and investigate its performance via simulations. We illustrate the use of such a selection procedure on some real data examples. The discussed examples include generalised normal, binomial and Poisson regression models.