Nonparametric statistics: smoothings methods

Teacher(s)

von Sachs Rainer;

Language

English

Main themes

Main themes The topics treated during this course are : 1. Nonparametric estimation of a distribution function 2. Nonparametric estimation of a density function : the kernel method 3. Nonparametric estimation of a regression function : - kernel estimation - local polynomial estimation - spline estimation The material will essentially be treated from an applied point of view of methodology. The student will study software applications of the proposed methods.

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 into nonparametric curve estimation: density estimation, nonparametric regression, kernel method, splines, local polynomials, bandwidth selection, estimation of derivatives, boundary treatments, multivariate aspects; comparison of different estimators via bias, variance and MSE. 

Teaching methods

The course material is taught during classroom lectures completed by an R-tutorial.

Evaluation methods

A simulation project has to be prepared (in R) during the semester. An oral exam on the material of the course completes the evaluation.

Other information

Prerequisites Basic knowledge about probability and statistics: descriptive statistics, calculating probabilities, distribution function, probability density, means, variances (conditionally or not), linear regression. It is advisable (but not necessary) to follow the course STAT2140 before.

Bibliography

Fan, J. et Gijbels, I. (1996). Local polynomial modelling and its applications. Chapman & Hall, New York.
Green, P.J. et Silverman, B.W. (2000). Nonparametric regression and generalized linear models. Chapman & Hall, New York.
HÄRDLE, W. (1990): Applied Nonparametric Regression. Cambridge University Press, Cambridge.
Hart, J.D. (1997). Nonparametric smoothing and lack-of-fit tests. Springer, New York.
Loader, C. (1999). Local regression and likelihood. Springer, New York.
Silverman, B.W. (1986) : Density Estimation for Statistics and Data Analysis. Chapman and Hall, London.
Simonoff, J.S. (1996). Smoothing methods in Statistics. Springer.

Teaching materials

• transparents sur moodle

Faculty or entity

LSBA