Optimal sup-norm rates, adaptivity and inference in nonparametric instrumental variables estimation

Xiaohong Chen () and Timothy M. Christensen
Additional contact information
Timothy M. Christensen: Institute for Fiscal Studies

No CWP32/15, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

Abstract: This paper makes several contributions to the literature on the important yet difficult problem of estimating functions nonparametrically using instrumental variables. First, we derive the minimax optimal sup-norm convergence rates for nonparametric instrumental variables (NPIV) estimation of the structural function h0 and its derivatives. Second, we show that a computationally simple sieve NPIV estimator can attain the optimal sup-norm rates for h0 and its derivatives when h0 is approximated via a spline or wavelet sieve. Our optimal sup-norm rates surprisingly coincide with the optimal L2-norm rates for severely ill-posed problems, and are only up to a [log(n)]? (with ?

Keywords: Ill-posed inverse problems; Series 2SLS; Optimal sup-norm convergence rates; Adaptive estimation; Random matrices; Bootstrap uniform confidence bands; Nonlinear welfare functionals; Nonparametric demand analysis with endogeneity (search for similar items in EconPapers)
Date: 2015-06-30
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (13)

Downloads: (external link)
https://www.ifs.org.uk/uploads/cemmap/wps/cwp321515.pdf (application/pdf)
Our link check indicates that this URL is bad, the error code is: 404 Not Found (https://www.ifs.org.uk/uploads/cemmap/wps/cwp321515.pdf [302 Found]--> https://ifs.org.uk/uploads/cemmap/wps/cwp321515.pdf)

Related works:
Working Paper: Optimal Sup-norm Rates, Adaptivity and Inference in Nonparametric Instrumental Variables Estimation (2015)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ifs:cemmap:32/15

Ordering information: This working paper can be ordered from
The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE

Access Statistics for this paper

More papers in CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE. Contact information at EDIRC.
Bibliographic data for series maintained by Emma Hyman ().