# APTS module: Flexible Regression

Module leader: C Miller and T Neocleous

Please see the full Module Specifications for background information relating to all of the APTS modules, including how to interpret the information below.

Aims: The term 'flexible regression' refers to a wide range of methods which provide flexibility in the nature of the relationship being modelled. The course will start with univariate smoothing and progress through standard forms of nonparametric regression to state-of-the art modelling tools which can be applied in a wide variety of settings. The course will cover the main ideas from a conceptual perspective as well as investigating aspects of the underlying theory and computation. There will also be some exploration of practical use of the methods in real applications.

Learning outcomes: By the end of the module, students will: be able to describe and explain the techniques of nonparametric regression including smoothing and quantile regression approaches; be able to describe the issues of bias and variance associated with model fitting and selection; be able to state and describe a range of mechanisms which can be used to smooth data; be able to explain how these techniques can be incorporated into wider modelling tools; be able to use these methods in a wide range of applications.

Prerequisites: Linear models and generalised linear models (preliminary APTS material and Statistical Modelling); R programming (preliminary APTS material and Statistical Computing); matrix computations (Statistical Computing); confidence intervals and hypothesis tests (Statistical Inference).

• Koenker, R. (2005). Quantile Regression (Econometric Society Monographs). Cambridge: Cambridge University Press. https://doi.org/10.1017/CBO9780511754098
• Wood, S.N. (2017) Generalized Additive Models: An Introduction with R (2nd edition). Chapman and Hall/CRC.

Topics:

• spline, basis and kernel approaches to nonparametric regression;
• quantile regression;
• computational issues and an insight into asymptotic properties;
• generalised additive models (including quantile regression extensions);
• alternative approaches, including eg functional data analysis and Gaussian processes;
• case studies.

Assessment: A set of exercises assigned by the module leaders, including a data-analysis exercise involving practical use of some of the methods covered.