Laguerre basis for inverse problems related to nonnegative random variables

Fabienne Comte (Université Paris Descartes)
Wednesday, February 1, 2017 - 10:00am
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

I will present, through two main examples, the specific properties of the Laguerre basis and show that it is a very convenient tool to solve estimation problems on R+. The first example is the regression-convolution model: an estimator of the unknown underlying function is built in two steps (deconvolution step, regression step) which are explained and discussed. Then, a risk study is conducted, that shows as usual that a bias-variance tradeoff must be performed. A model selection device is shown to solve this question. The second example concerns a simpler multiplicative model, for which a projection estimators of the density of the hidden variables are built and discussed. The specific properties of the Laguerre basis with respect to these solutions are enhanced. Rates of convergence in relation with Sobolev-Laguerre spaces are presented. To conclude, several other problems solved with the Laguerre bases are listed.
This presentation relies on several joint works with different group of co-authors (D. Belomenstny and V. Genon-Catalot; C.-A. Cuenod, M. Pensky and Y. Rozenholc; C. Dion; V. Genon-Catalot).