Basic Concepts for Smoothing and Semiparametric Regression

This chapter reviews basic concepts for smoothing and semiparametric regression based on roughness penalties or — from a Bayesian perspective — corresponding smoothness priors. In particular, it introduces several tools for statistical modelling and inference that will be utilized in later chapters. It also highlights the close relation between frequentist penalized likelihood approaches and Bayesian inference based on smoothness priors. The chapter is organized as follows. Section 2.1 considers the classical smoothing problem for time series of Gaussian and non-Gaussian observations. Section...

This chapter reviews basic concepts for smoothing and semiparametric regression based on roughness penalties or — from a Bayesian perspective — corresponding smoothness priors. In particular, it introduces several tools for statistical modelling and inference that will be utilized in later chapters. It also highlights the close relation between frequentist penalized likelihood approaches and Bayesian inference based on smoothness priors. The chapter is organized as follows. Section 2.1 considers the classical smoothing problem for time series of Gaussian and non-Gaussian observations. Section 2.2 introduces penalized splines and their Bayesian counterpart as a computationally and conceptually attractive alternative to random-walk priors. Section 2.3 extends the univariate smoothing approaches to additive and generalized additive models.