Asymptotic statisticsLe Cam’s theory of asymptotic experiments plays a key role in many of my papers. Contiguity, local asymptotic normality, convergence of sequences of experiments and their impact, on the construction of optimal statistical procedures are my main interests there.
High dimensionsI recently began working on problems where the number p of variables is large compared to the sample size n. In a hypothesis context, I do not restrict to null (n,p)-asymptotic results, but I also consider asymptotic non-null and optimality issues.
Directional statisticsThis topic addresses inference problems involving observations on the p-dimensional unit sphere. This arises in applications where only directions of the observations from a given centre are relevant (so that their distances from this centre may be discarded).
Nonparametric statisticsI have always been interested in nonparametric inference, with special emphasis on hypothesis testing. In this framework, many of my papers developed rank tests for problems belonging to multivariate analysis. Under ellipticity assumptions, we showed that robustness and Le Cam optimality can be combined.
Depth-based methodsStatistical depth measures centrality of a point in the sample space with respect to a probability distribution. In this context, my research focuses on defining new depth concepts and on developing inference methods based on depth.
Multivariate quantilesPart of my research has been dedicated to the possible extensions of the concept of quantile to the multivariate setup. On the agenda has been the companion problem to define concepts of multiple-output regression quantiles. In both cases, we are after concepts that maintain the strong links between quantiles and statistical depth.