A brief history of weak dependencies

More than a purely formal exposition, the aim is to demonstrate the advantages and disadvantages of each of the most commonly used concepts, depending on the intended purpose and the types of models involved. Recently, Wu proposed asymptotic results that improve upon virtually everything imaginable, with speeds corresponding to those known to be optimal in the independent framework. The price to pay is the representation of such models, necessarily discrete-time, as functions of a sequence of independent variables, for which coefficients and couplings, technically somewhat unnatural, can be determined. I will attempt to highlight all the advantages of these techniques, as well as developments for models used in statistical practice.

I was the advisor for 20 PhD or Habilitation theses with around 9000 google citations and I developed a strong group on dependence. For my work I was granted as a member of the very selective French University Institute. Now I am Emeritus professor at Cergy University.

I aim at understanding, analysing and fitting new dependent random models in order to study their probabilistic and ergodic properties, but also to fit and test them, including integer valued and high dimensional models. I am involved into dependences such as strong mixing or long range dependence. Weak dependence introduced in 1996 with Sana Louhichi relaxes mixing conditions. I also introduced wavelets in statistics which knew a huge developments. 

For more information about the ESD Seminar, please email esd_invite@sutd.edu.sg