arXiv 5 Nov 2014 · Mathematics — Statistics Theory · publishedEconometrica (2015) · 108 citations (OpenAlex)
arXiv:1411.1144 · PDF · DOI · OpenAlex · Extracted main text
This paper considers inference on functionals of semi/nonparametric conditional moment restrictions with possibly nonsmooth generalized residuals, which include all of the (nonlinear) nonparametric instrumental variables (IV) as special cases. These models are often ill-posed and hence it is difficult to verify whether a (possibly nonlinear) functional is root-$n$ estimable or not. We provide computationally simple, unified inference procedures that are asymptotically valid regardless of whether a functional is root-$n$ estimable or not. We establish the following new useful results: (1) the asymptotic normality of a plug-in penalized sieve minimum distance (PSMD) estimator of a (possibly nonlinear) functional; (2) the consistency of simple sieve variance estimators for the plug-in PSMD estimator, and hence the asymptotic chi-square distribution of the sieve Wald statistic; (3) the asymptotic chi-square distribution of an optimally weighted sieve quasi likelihood ratio (QLR) test under the null hypothesis; (4) the asymptotic tight distribution of a non-optimally weighted sieve QLR statistic under the null; (5) the consistency of generalized residual bootstrap sieve Wald and QLR tests; (6) local power properties of sieve Wald and QLR tests and of their bootstrap versions; (7) asymptotic properties of sieve Wald and SQLR for functionals of increasing dimension. Simulation studies and an empirical illustration of a nonparametric quantile IV regression are presented.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Blundell, R., Chen, X., and Kristensen, D (2007) Semi-nonparametric iv estimation of shape invariant engel curves self | 1.000 | 12 | 4 | 100% |
| 2 | Newey, W. and Powell, J (2003) Instrumental variables estimation for nonparametric models | 1.000 | 5 | 3 | 100% |
| 3 | Chen, X. and Pouzo, D (2012) Estimation of nonparametric conditional moment models with possibly nonsmooth generalized residuals self | 0.925 | 24 | 8 | 79% |
| 4 | Chen, X. and Pouzo, D (2009) Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals self | 0.891 | 24 | 10 | 71% |
| 5 | Ai, C. and Chen, X (2007) Estimation of possibly misspecified semiparametric conditional moment restriction models with different conditioning variables self | 0.874 | 6 | 3 | 67% |
| 6 | Ai, C. and Chen, X (2003) Efficient estimation of models with conditional moment restrictions containing unknown functions self | 0.858 | 19 | 8 | 63% |
| 7 | Chen, X., Linton, O., and van Keilegom, I (2003) Estimation of semiparametric models with the criterion functions is not smooth self | 0.737 | 4 | 4 | 50% |
| 8 | Chamberlain, G (1992) Efficiency bounds for semiparametric regression | 0.737 | 4 | 2 | 75% |
| 9 | Graham, B. and Powell, J (2012) Identification and estimation of average partial effects in irregular correlated random coefficient panel data models | 0.737 | 4 | 2 | 75% |
| 10 | Horowitz, J (2011) Applied nonparametric instrumental variables estimation | 0.737 | 3 | 2 | 100% |
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