Adaptive M-Estimation

In the time from february 28th. until march 12th. 2005 Prof. J.M. Loubes gave an intensive course consisting of eight lectures and exercises about "Adaptive M-Estimation". The lecture took place in the Seminarraum of the Institute of Mathematical Stochastics (IMS).


Abstract

"Adaptive estimation is concerned with the estimation of a signal when no prior assumption is made on the regularity of the observed functions. Yet, the estimator must be optimal, with regards to it´s rate of convergence. The function to be estimated can be directly observed (direct estimation) or observed through the image of a non invertible operator (inverse problem). The estimators we will construct will use wavelet basis and model selection theory. Applications abound in almost all areas of science and technology, including economics, geology, hydrology, medical imaging, signal processing and meteorology."