Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/79392 
Year of Publication: 
2007
Series/Report no.: 
cemmap working paper No. CWP20/07
Publisher: 
Centre for Microdata Methods and Practice (cemmap), London
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.
Subjects: 
Nonparametric instrumental regression , Nonparametric indirect regression , Statistical ill-posed inverse problems , Minimax risk lower bound , Optimal rate
JEL: 
C14
C30
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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