Component identification and estimation in nonlinear high-dimensional regression models by structural adaptation Samarov, Alexander ∗ University of Massachusetts-Lowell and Massachusetts Institute of Technology. 77 Massachusetts Avenue, Cambridge, MA 02139-4307, U.S.A. samarov@mit.edu Spokoiny, Vladimir Weierstrass Institute and Humboldt University, Mohrenstr. 39, 10117 Berlin, Germany spokoiny@wias-berlin.de Vial, Celine Centre for Mathematics and its Applications, ANU, Canberra, ACT 0200, Australia celine.vial@maths.anu.edu.au ∗ Part of this research was done while the first author, AS, visited Tel Aviv University on a Fulbright award; their support is gratefully acknowledged. AS was also supported by the NSF grant DMS-9971579 and by the eBusiness center at MIT. 1