ABSTRACT
In some applications, there may be a theoretical basis for a particular form of nonlinearity, though some elements of specification will be uncertain – see M. Borsuk and C. Stow on biochemical oxygen demand, and K. Meyer and B. Millar on models of fishery stock. This chapter explores extending non-parametric regression to multiple predictors raises the same issues as multiple linear regressions, for example, whether interactions are necessary and how the presence of smooths for other predictors alters the smooth for a given predictor. It discusses the robustness in non-parametric regression may be obtained through spatially adaptive methods which allow the level of smoothness to vary over the space of the covariates. The chapter describes a major application area for non-parametric regression is in longitudinal settings. Non-parametric regressions are often heavily parameterised and parameter redundancies are likely, indicating that selection among predictor effects, including smooths, is necessary.
