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.