The main topics of this research are empirical processes and bootstrap. The investigator will consider applications of the limit theorems of empirical processes in statistics, in particular to the asymptotics of M-estimators and U-quantiles. He also will consider the "rates of convergence" in some limit theorems, such us the rate of convergence of the bootstrap central limit theorem of U-quantiles and the Bahadur--Kiefer representations for M-estimators. One problem, which he is exploring, is the study of the central (and non-central) limit theorems for empirical processes under long range dependence. This research is in statistics and probability. Probability theory will be used to learn how to deal with data which is not independent. Some applications to statistics which will be considered are the study of the speed of convergence of certain estimators and of certain statistical procedures.
