Format:
1 Online-Ressource (25 Seiten)
Content:
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 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.
Content:
Peer Reviewed
Note:
This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.
In:
Cambridge : Cambridge Univ. Press, 27,3, Seiten 497-521
Language:
English
DOI:
10.1017/S0266466610000381
URN:
urn:nbn:de:kobv:11-110-18452/28456-1
URL:
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