Robust statistical methods and applications.
The goal of robust statistics is to develop data analytical
methods which are resistant to outlying observations in the data,
and hence which are also able to detect these outliers. Pioneering
work in this area has been done by Huber (1981), Hampel et al.
(1986) and Rousseeuw and Leroy (1987). In their work, estimators
for location, scale, scatter and regression play a central role.
They assume that the majority of the data follow a
parametric model, whereas a minority (the contamination) can take
arbitrary values. This approach leads to the concept of the
influence function of an estimator which measures the influence of
a small amount of contamination in one point. Other measures of
robustness are the finite-sample and the asymptotic breakdown
value of an estimator. They tell what the smallest amount of
contamination is which can carry the estimates beyond all bounds.
Nowadays, robust estimators are being developed for many
statistical models. Our research group is very active in
investigating estimators of covariance and regression for
high-dimensional data, with applications in chemometrics and
bio-informatics. Recently, robust estimators have been developed
for PCA (principal component analysis), PCR (principal component
regression), PLS (partial least squares), classification, ICA
(independent component analysis) and multi-way analysis. Also
robust measures of skewness and tail weight have been introduced.
We study robustness of kernel methods, and regression quantiles
for censored data.
Semiparametric and nonparametric statistical inference and applications.
The aim of statistical analysis of data is to provide answers to
questions regarding the population from which the data are collected.
Parametric statistical analysis rely on prior information
about the population and hence in parametric analysis one can focus on a limited number
of parameters that need to be studied. Often however such prior
information is not available or only very limited assumptions are
justifiable (for example from knowleghde gained by previous studies). Nowadays very powerful nonparametric and
semiparametric statistical methods are available, and present a
whole toolbox of flexible methods for statistical analysis in almost all areas of applications. They
are also implemented in the main software packages and/or are provided in separate toolboxes. The
development of new and more sophisticated ways of collecting data
resulted in many very challenging problems to be faced for
statistical researches. Examples include very high dimensional
data (e.g. in genetics, in chemiometrics, ...), data of complex
structures (financial data involving e.g. very rapid changes, many
simultaneously observed correlated time series; (sequences) of 3D
images, satellite images, ....). Such complex structures require often a completely different type of methods which need to be developed.
More information will appear here soon (under construction).
List of major research projects and networks (coordinating and/or participating):
Bilateral agreement with South Africa, Project 04/45 (Bilateraal
Akkoord) on "Statistical Inference for dependent and censored
data" (J. Beirlant, K.U.Leuven; P. Janssen and N. Veraverbeke,
Univ. of Hasselt, and Daan de Waal, Univ. of Free State, South
Africa, and Jan Swanepoel, Univ. of North West, South Africa),
2005-2006.
FWO research project G.0499.04 on "Integration of parametric
robust methods and non-parametric kernel based methods".
(Promotors: B. De Moor, M. Hubert and J. Suykens, K.U.Leuven),
2004-2007.
FWO research project, G.02080.06 on "Modern perspectives in claim
reserving problem for non-life sector" (J. Dhaene, J. Beirlant,
K.U.Leuven), 2006-2009.
GOA -research project on "Actuarial, Financial and Statistical
Aspects of Dependencies in insurance and actuarial portfolios''
(J. Beirlant, J. Dhaene, M. Goovaerts, J. Teugels, K.U.Leuven),
(University Research Fund), 2001-2006.
GOA-research project on "Nonparametric and semiparametric
techniques and robust methods in statistical analysis", (I.
Gijbels, G. Claeskens, C. Croux and M. Hubert), (University
Research Fund), 10/2006-2011.
