Arbeitspapier
Optimal uniform convergence rates for sieve nonparametric instrumental variables regression
We study the problem of nonparametric regression when the regressor is endogenous, which is an important nonparametric instrumental variables (NPIV) regression in econometrics and a difficult ill-posed inverse problem with unknown operator in statistics. We first establish a general upper bound on the sup-norm (uniform) convergence rate of a sieve estimator, allowing for endogenous regressors and weakly dependent data. This result leads to the optimal sup-norm convergence rates for spline and wavelet least squares regression estimators under weakly dependent data and heavy-tailed error terms. This upper bound also yields the sup-norm convergence rates for sieve NPIV estimators under i.i.d. data: the rates coincide with the known optimal L2- norm rates for severely ill-posed problems, and are power of log (n) slower than the optimal L2- norm rates for mildly ill-posed problems. We then establish the minimax risk lower bound in sup-norm loss, which coincides with our upper bounds on sup-norm rates for the spline and wavelet sieve NPIV estimators. This sup-norm rate optimality provides another justification for the wide application of sieve NPIV estimators. Useful results on weakly-dependent random matricies are also provided.
- Language
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Englisch
- Bibliographic citation
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Series: cemmap working paper ; No. CWP56/13
- Classification
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Wirtschaft
Estimation: General
Semiparametric and Nonparametric Methods: General
Multiple or Simultaneous Equation Models: Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
- Subject
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Nonparametric instrumental variables
Statistical ill-posed inverse problems
Optimal uniform convergence rates
Weak dependence
Random matrices
Splines
Wavelets
- Event
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Geistige Schöpfung
- (who)
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Chen, Xiaohong
Christensen, Timothy
- Event
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Veröffentlichung
- (who)
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Centre for Microdata Methods and Practice (cemmap)
- (where)
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London
- (when)
-
2013
- DOI
-
doi:10.1920/wp.cem.2013.5613
- Handle
- Last update
-
10.03.2025, 11:45 AM CET
Data provider
ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften - Leibniz-Informationszentrum Wirtschaft. If you have any questions about the object, please contact the data provider.
Object type
- Arbeitspapier
Associated
- Chen, Xiaohong
- Christensen, Timothy
- Centre for Microdata Methods and Practice (cemmap)
Time of origin
- 2013
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