Smoothing techniques

Teacher(s)

Kiriliouk Anna;

Language

English

Prerequisites

Concepts and tools equivalent to those taught in the teaching units :
•    LSTAT2120 Linear models
•    LDATS2030 Programming and data reporting in R

Main themes

This is the second general training course in nonparametric statistics, focusing on smoothing methods: nonparametric estimation of a density function and a regression function (using the kernel method, local polynomial estimation and splines) and generalised additive models.

Learning outcomes

At the end of this learning unit, the student is able to :
1	Second course of general education in nonparametric statistics, which mainly focuses on smoothing methods.

Content

Introduction to nonparametric statistics, focusing mainly on non-parametric smoothing methods: density estimation (kernel method); nonparametric regression (kernel method, nearest neighbours, local polynomials); spline-based smoothing; Generalized Additive Models; theoretical aspects (comparison of different estimation methods using bias, variance, MSE).
These topics are mainly covered from a methodological point of view, with illustrations on real data using the statistical programming language R. 

Teaching methods

The course material is taught during classroom lectures completed by three R tutorials.

Evaluation methods

During the examination period: written exam, with some questions to be completed on a computer.

Other information

Prerequisites. Basic knowledge about probability and statistics: descriptive statistics, calculating probabilities, cumulative distribution function, probability density function, means, variances, linear regression. 

Online resources

https://moodle.uclouvain.be/course/view.php?id=2395

Bibliography

Fan, J. et Gijbels, I. (1996). Local polynomial modelling and its applications. Chapman & Hall.
Green, P.J. et Silverman, B.W. (2000). Nonparametric regression and generalized linear models. Chapman & Hall.
Härdle, W. (1990): Applied Nonparametric Regression. Cambridge University Press.
Simonoff, J.S. (1996). Smoothing methods in Statistics. Springer.
García-Portugués, E. (2025). Notes for Nonparametric Statistics. Version 6.12.1. Available at https://bookdown.org/egarpor/NP-UC3M/.
Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning. Springer. 
Hastie, T. & Tibshirani, R., (1990). Generalized Additive Models. Chapman and Hall.
Wood, S.N. (2017). Generalized Additive Models: an Introduction with R. CRC Press.
 

Teaching materials

• Slides on moodle

Faculty or entity

> LSBA