Unit name | Nonparametric Regression |
---|---|

Unit code | MATHM6004 |

Credit points | 10 |

Level of study | M/7 |

Teaching block(s) |
Teaching Block 1A (weeks 1 - 6) |

Unit director | Dr. Kovac |

Open unit status | Not open |

Pre-requisites |
MATH35110 Linear Models |

Co-requisites |
None |

School/department | School of Mathematics |

Faculty | Faculty of Science |

Unit aims

Teach the problem of nonparametric function estimation Introduce several methods like kernel estimators and spline techniques Construct estimators of a signal from a sample of observations Learn flexible and popular techniques of distribution-free methods General Description of the Unit

A regression function is an important tool for describing the relation between two or more random variables. In real life problems, this function is usually unknown but can be estimated from a sample of observations. In the most simple cases, we have enough information on the problem at hand to assume that the regression curve is known up to the value of some coefficients (for example, it is a straight line, but we need to estimate the coefficients of the line). Nonparametric methods are flexible techniques dedicated to treat more general cases: here, we construct a good estimator of the regression function without assuming that it has a specified shape. In this module, we will introduce popular nonparametric methods of regression estimation: kernel estimators, spline regression, wavelet thresholding and shape-restricted regression. We will see how these methods can be applied in practice.

Each module covers an area of statistics and applied probability relevant to the research and other interests of members of academic staff. Details are given in the Syllabus section below.

Further information is available on the School of Mathematics website: http://www.maths.bris.ac.uk/study/undergrad/

Learning Objectives

The students will be able to:

- calculate nonparametric regression estimates in R
- decide on suitable techniques for choosing smoothing parameters involved in *techniques for nonparametric regression
- compute the various nonparametric regression estimators for given data
- know the strengths and weaknesses of the various methods introduced
- be able to decide the most appropriate method to use given the data at hand

Transferable Skills

In addition to the general skills associated with other mathematical units, students will also have the opportunity to gain practice in the following: report writing, use of information resources, use of initiative in learning material in other than that provided by the lectures themselves, time management, general IT skills and word-processing.

Lectures supported by exercise sheets, many of which involve computer practical work.

100% Coursework (project).

The homework will be marked against the criteria on the 0-100 scale.

The main references are:

- J. Fan and I. Gijbels. (1996) Local Polynomial Modeling and Its Applications. Chapman & Hall, London
- Haerdle, W. (1992) Applied nonparametric regression. Econometric Society Monographs.
- Nason, G. (2008) Wavelet Methods in Statistics with R. Springer.
- Wand, M.P and Jones, M.C. (1995). Kernel smoothing.

but the following books can also be helpful:

- Bowman, A.W. and Azzalini, A. (1997), Applied smoothing techniques for data analysis
- Haerdle, W. (1991) Smoothing techniques : with implementation in S