Document Type
Discussion Paper
Publication Date
9-1-2007
CFDP Number
1626
CFDP Pages
27
Abstract
In this paper, we clarify the relations between the existing sets of regularity conditions for convergence rates of nonparametric indirect regression (NPIR) and nonparametric instrumental variables (NPIV) regression models. We establish minimax risk lower bounds in mean integrated squared error loss for the NPIR and the NPIV models under two basic regularity conditions that allow for both mildly ill-posed and severely ill-posed cases. 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.
Recommended Citation
Chen, Xiaohong and Reiss, Markus, "On Rate Optimality for Ill-posed Inverse Problems in Econometrics" (2007). Cowles Foundation Discussion Papers. 1924.
https://elischolar.library.yale.edu/cowles-discussion-paper-series/1924