EconBase
← All papers

Penalized Sieve GEL for Weighted Average Derivatives of Nonparametric Quantile IV Regressions

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

Abstract

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.

Citation extraction

46
references
108
in-text mentions
46
distinct cited
1
self-citations
12,880
main-text words

appendix boundary found by appendix_command · 45% of the source is main text. Read the extracted text to check this.

Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1S G Donald, G W Imbens, and W K Newey (2003) Empirical likelihood estimation and consistent tests with conditional moment restrictions1.000103100%
2X Chen and D Pouzo (2015) Sieve wald and qlr inferences on semi/nonparametric conditional moment models1.00073100%
3X Chen and D Pouzo (2012) Estimation of nonparametric conditional moment models with possibly nonsmooth generalized residuals1.00064100%
4C Ai and X Chen (2012) The semiparametric efficiency bound for models of sequential moment restrictions containing unknown functions1.00053100%
5T. Severini and G. Tripathi (2012) Efficiency bounds for estimating linear functionals of nonparametric regression models with endogenous regressors0.9285380%
6C Ai and X Chen (2003) Efficient estimation of models with conditional moment restrictions containing unknown functions0.81142100%
7W K Newey and T M Stoker (1993) Efficiency of weighted average derivative estimators and index models0.81142100%
8P Bickel, C Klaassen, Y Ritov, and J Wellner (1998) Efficient and adaptive estimation for semiparametric models0.7374275%
9A. W. Van der Vaart (2000) Asymptotic statistics, volume 30.7373367%
10R Blundell, X Chen, and D Kristensen (2007) Semi-nonparametric iv estimation of shape-invariant engel curves0.73732100%

Showing the top 10 of 46 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Efficient Estimation of Average Derivatives in NPIV Models: Simulation Comparisons of Neural Network Estimators0.40511
2Adversarial Estimators0.40511
3On Gaussian Process Priors in Nonparametric Conditional Moment Restriction Models0.40511
4Thin Sets Are Not Equally Thin: Minimax Learning of Submanifold Integrals0.40511
5Generalized Bayes in Conditional Moment Restriction Models0.40511