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

Xiaohong Chen () and Timothy M. Christensen
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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
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Working Paper: Optimal Sup-norm Rates, Adaptivity and Inference in Nonparametric Instrumental Variables Estimation (2015) Downloads
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