5. Smoothing: Local Regression Techniques

**Catherine Loader
**

Smoothing methods attempt to find functional relationships between different measurements. As in the standard regression setting, the data is assumed to consist of measurements of a response variable, and one or more predictor variables. Standard regression techniques (Chap. III8.) specify a functional form (such as a straight line) to describe the relation between the predictor and response variables. Smoothing methods take a more flexible approach, allowing the data points themselves to determine the form of the fitted curve.

This article begins by describing several different approaches to smoothing, including kernel methods, local regression, spline methods and orthogonal series. A general theory of linear smoothing is presented, which allows us to develop methods for statistical inference, model diagnostics and choice of smoothing parameters.

The theory is then extended to more general settings, including multivariate smoothing and likelihood models.

- 5.1 Smoothing
- 5.2 Linear Smoothing
- 5.2.1 Kernel Smoothers
- 5.2.2 Local Regression
- 5.2.3 Penalized Least Squares (Smoothing Splines)
- 5.2.4 Regression Splines
- 5.2.5 Orthogonal Series

- 5.3 Statistical Properties of Linear Smoothers

- 5.4 Statistics for Linear Smoothers: Bandwidth Selection and Inference

- 5.5 Multivariate Smoothers