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We establish minimax risk lower bounds in mean integrated squared error loss for the NPIR and NPIV models under two basic regularity conditions: the approximation number and the link condition. We show that both a simple projection estimator for the NPIR model and a sieve minimum distance estimator for the NPIV model can achieve the minimax risk lower bounds and are rate optimal uniformly over a large class of structure functions, allowing for mildly ill-posed and severely ill-posed cases.<\/jats:p>","DOI":"10.1017\/s0266466610000381","type":"journal-article","created":{"date-parts":[[2010,10,11]],"date-time":"2010-10-11T08:35:25Z","timestamp":1286786125000},"page":"497-521","source":"Crossref","is-referenced-by-count":71,"title":["ON RATE OPTIMALITY FOR ILL-POSED INVERSE PROBLEMS IN ECONOMETRICS"],"prefix":"10.1017","volume":"27","author":[{"given":"Xiaohong","family":"Chen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Markus","family":"Reiss","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2010,10,11]]},"reference":[{"key":"S0266466610000381_ref30","doi-asserted-by":"crossref","first-page":"1564","DOI":"10.1214\/aos\/1017939142","article-title":"Information-theoretic determination of minimax rates of convergence","volume":"27","author":"Yang","year":"1999","journal-title":"Annals of Statistics"},{"key":"S0266466610000381_ref27","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/21\/6\/003"},{"key":"S0266466610000381_ref24","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-2712-0"},{"key":"S0266466610000381_ref23","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466610000393"},{"key":"S0266466610000381_ref20","doi-asserted-by":"publisher","DOI":"10.1214\/009053605000000714"},{"key":"S0266466610000381_ref14","volume-title":"Spectral Theory and Differential Operators","author":"Edmunds","year":"1987"},{"key":"S0266466610000381_ref11","unstructured":"Darolles S. , Florens J.-P. , & Renault E. 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