Here are some of our main current research themes.
Asymptotic theoryAsymptotic inference is integral part of the research of several members in our group. In particular, Le Cam's theory of asymptotic experiments plays a key role. Contiguity, local asymptotic normality, convergence of statistical experiments and their impact on the construction of optimal statistical procedures are the main interests there. We also work on classical limit theorems for partial sums of empirical processes and their statistical applications, e.g., in change point detection.
Directional statisticsDirectional statistics, where observations are directions, that is, points on the p-dimensional unit spheres, is a field that has attracted much attention in the past two decades. Initially motivated by geological and wind direction data, that are low-dimensional (p=2,3), directional statistics now is also increasingly concerned with high dimensions, e.g., for text mining. We develop statistical procedures for directional inference problems, both in the low- and high-dimensional setups.
Functional data analysisSince storing data is steadily becoming easier and cheaper we are nowadays quite often collecting nearly continuous data records. Functional data analysis is an emerging statistical discipline which aims to extract information from such complex, high-dimensional data objects. We are particularly interested in problems which arise when functional data are collected sequentially in time and hence exhibit temporal dependence.
High dimensionsWe consider problems where the number p of variables is large compared to the sample size n. Part of our research in this context considers (n,p)-asymptotic inference for testing problems that are also standard in multivariate statistics (such as, e.g., the problem of testing for sphericity). A second theme in high dimensions focuses on sparse and structured variable selection, through the use and optimisation of information criteria.
Nonparametric smoothingWe work on combinations of local estimators and estimators in a multiscale basis, leading to multiscale local polynomial decompositions, where bandwidths play the role of a user controled scale parameters. Another topic of research is the incorporation of splines on irregularly spaced knots into a wavelet decomposition.
Semi- and nonparametricsOur research in semiparametric statistics has been mainly dealing with rank-based hypothesis testing. Our research activity in nonparametric statistics has been very diverse. In particular, we have been working on ... Robust nonparametric statistics has also been much considered, with particular emphasis on statistical depth and multivariate quantiles.
Times series analysisWe have a long tradition in time series analysis. Nowadays, the main research efforts in this direction focus on the analysis and prediction of large panels of time series, in particular in the framework of the generalized dynamic factor model, on functional time series, and on time series models with time-varying coefficients.