ABSTRACT
This chapter introduces some non-parametric estimation methods that are useful to model complex relationships between the explanatory variables and the response. Many applications in statistics require that the model is flexible in a way that makes the relationship between the response and the covariates non-linear. A first approach to developing a smooth function to fit the lidar dataset is by using linear combinations of smooth functions on the covariates. Polynomials are too rigid to obtain good local smoothing and the smooth term produced will fit different parts of the dataset with different accuracy. In particular, splines are a popular option when it comes to producing smooth terms with local smoothing. Local smoothing is determined by the number and location of the knots, and they must be chosen with care. For the case of irregularly spaced data or knots, it is possible to build smooth terms using other latent effects in integrated nested Laplace approximation.
