Xiaohong Chen, Demian Pouzo, James L. Powell
arXiv 26 Feb 2019 · Mathematics — Statistics Theory · publishedJournal of Econometrics (2019) · 4 citations (OpenAlex)
arXiv:1902.10100 · PDF · DOI · OpenAlex · Extracted main text
This paper considers estimation and inference for a weighted average derivative (WAD) of a nonparametric quantile instrumental variables regression (NPQIV). NPQIV is a non-separable and nonlinear ill-posed inverse problem, which might be why there is no published work on the asymptotic properties of any estimator of its WAD. We first characterize the semiparametric efficiency bound for a WAD of a NPQIV, which, unfortunately, depends on an unknown conditional derivative operator and hence an unknown degree of ill-posedness, making it difficult to know if the information bound is singular or not. In either case, we propose a penalized sieve generalized empirical likelihood (GEL) estimation and inference procedure, which is based on the unconditional WAD moment restriction and an increasing number of unconditional moments that are implied by the conditional NPQIV restriction, where the unknown quantile function is approximated by a penalized sieve. Under some regularity conditions, we show that the self-normalized penalized sieve GEL estimator of the WAD of a NPQIV is asymptotically standard normal. We also show that the quasi likelihood ratio statistic based on the penalized sieve GEL criterion is asymptotically chi-square distributed regardless of whether or not the information bound is singular.
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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 | S G Donald, G W Imbens, and W K Newey (2003) Empirical likelihood estimation and consistent tests with conditional moment restrictions | 1.000 | 10 | 3 | 100% |
| 2 | X Chen and D Pouzo (2015) Sieve wald and qlr inferences on semi/nonparametric conditional moment models | 1.000 | 7 | 3 | 100% |
| 3 | X Chen and D Pouzo (2012) Estimation of nonparametric conditional moment models with possibly nonsmooth generalized residuals | 1.000 | 6 | 4 | 100% |
| 4 | C Ai and X Chen (2012) The semiparametric efficiency bound for models of sequential moment restrictions containing unknown functions | 1.000 | 5 | 3 | 100% |
| 5 | T. Severini and G. Tripathi (2012) Efficiency bounds for estimating linear functionals of nonparametric regression models with endogenous regressors | 0.928 | 5 | 3 | 80% |
| 6 | C Ai and X Chen (2003) Efficient estimation of models with conditional moment restrictions containing unknown functions | 0.811 | 4 | 2 | 100% |
| 7 | W K Newey and T M Stoker (1993) Efficiency of weighted average derivative estimators and index models | 0.811 | 4 | 2 | 100% |
| 8 | P Bickel, C Klaassen, Y Ritov, and J Wellner (1998) Efficient and adaptive estimation for semiparametric models | 0.737 | 4 | 2 | 75% |
| 9 | A. W. Van der Vaart (2000) Asymptotic statistics, volume 3 | 0.737 | 3 | 3 | 67% |
| 10 | R Blundell, X Chen, and D Kristensen (2007) Semi-nonparametric iv estimation of shape-invariant engel curves | 0.737 | 3 | 2 | 100% |
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