APTS module: Nonparametric Smoothing
Module leader: R J Samworth
Previous module leader: A Delaigle (2007–8, 2008–9)
Please see the full Module Specifications 
document for background information relating to all of the APTS modules, including how to interpret the information below.
Aims: In nonparametric statistics, it is not assumed that data come from a distribution belonging to a finite-dimensional class. This module will introduce students to the theory and methods associated with the idea of smoothing, which is one of the key concepts in modern nonparametric techniques of statistical analysis.
Learning outcomes: By the end of the module, students will understand the technique of kernel density estimation and its advantages over histograms. They will appreciate the central role played by the smoothing parameter, or bandwidth, and understand how this can be determined in practice. Students will also understand how both kernel- and spline-based smoothing methods can be used to estimate a nonparametric regression function.
Prerequisites: Preparation for this module should include a rapid review of basic probabilistic limit theory (including modes of convergence, laws of large numbers, ’o’and ’O’ notation and the delta method), and basic understanding of asymptotic expansions — to at least the level of the earlier APTS module ‘Statistical Asymptotics’.
Topics:
- Kernel and spline approaches to smoothing;
- Determination of degree of smoothing (bandwidth, penalty, effective degrees of freedom);
- Density estimation;
- Nonparametric regression;
- Applications, e.g., covariate measurement error, generalized additive models.
- Connections with wavelets and other nonparamatric estimators.
Assessment: A set of exercises assigned by the module leader, or a data-analysis exercise involving practical use of some of the methods covered.
