The product of a high-flying summer school in Paris in 2009, this volume synthesises the state of the art on ill-posed statistical inverse problems and high-dimensional estimation and explores the ways these techniques can be applied to economics.

The Stats in the Château summer school was held at the CRC château on the campus of HEC Paris, Jouy-en-Josas, France, from August 31 to September 4, 2009. This event was organized jointly by faculty members of three French academic institutions ENSAE ParisTech, the Ecole Polytechnique ParisTech, and HEC Paris which cooperate through a scientific foundation devoted to the decision sciences.The scientific content of the summer school was conveyed in two courses, one by Laurent Cavalier (Université Aix-Marseille I) on "Ill-posed Inverse Problems", and one by Victor Chernozhukov (Massachusetts Institute of Technology) on "High-dimensional Estimation with Applications to Economics". Ten invited researchers also presented either reviews of the state of the art in the field or of applications, or original research contributions.This volume contains the lecture notes of the two courses. Original research articles and a survey complement these lecture notes. Applications to economics are discussed in various contributions.

An excellent review of the state of the art written by leaders in their domain Applications of recent estimation techniques to quantitative analysis in economics are performed The two lecture notes chapters can be used for a graduate course

Autorentext

Pierre Alquier is an associate professor at Université Paris 7 and a research fellow at CREST. He holds a PhD from Université Paris 6. His research themes are high dimensional estimation and agregation of estimators in statistics.

Eric Gautier is an associate professor at ENSAE ParisTech and a researcher at CREST. He holds a PhD from the University of Rennes 1. His research is both in probability and theoretical econometrics. Regarding the second theme, he is particularly interested in inverse problems and high dimensional estimation and their applications to economics.

Gilles Stoltz is a research fellow at CNRS, Ecole normale supérieure and an affiliated professor at HEC Paris. He holds a PhD and an habilitation from Université Paris-Sud, Orsay. His research themes concern sequential prediction of arbitrary sequences and its application to the theory of repeated games.

Inhalt
Part I Lecture Notes on Inverse Problems: Inverse Problems in Statistics (Laurent Cavalier).- Part II Invited Contribution on Inverse Problems: Non Parametric Models with Instrumental Variables (Jean-Pierre Florens).- Part III Lecture Notes on High-Dimensional Estimation: High Dimensional Sparse Econometric Models: An Introduction (Alexandre Belloni and Victor Chernozhukov).- Part IV Invited Contributions on High-Dimensional Estimation: Model selection in Gaussian regression for high-dimensional data (Felix Abramovich and Vadim Grinshtein).- Bayesian Perspectives on Sparse Empirical Bayes Analysis (SEBA) (Natalia Bochkina and Ya'acov Ritov).- Part V Invited and Contributed Talks Given During the Summer School: List of the Courses.- List of the Invited Talks.- List of the Contributed Talks and Posters.