DeepAI AI Chat
Log In Sign Up

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

02/26/2019
by   Xiaohong Chen, et al.
berkeley college
Yale University
0

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.

READ FULL TEXT
12/31/2022

Inference on Time Series Nonparametric Conditional Moment Restrictions Using General Sieves

General nonlinear sieve learnings are classes of nonlinear sieves that c...
08/07/2021

Culling the herd of moments with penalized empirical likelihood

Models defined by moment conditions are at the center of structural econ...
01/28/2021

Adaptive Estimation of Quadratic Functionals in Nonparametric Instrumental Variable Models

This paper considers adaptive estimation of quadratic functionals in the...
06/19/2020

Sparse Quantile Regression

We consider both ℓ _0-penalized and ℓ _0-constrained quantile regression...
12/23/2017

Distribution Regression

Linear regression is a fundamental and popular statistical method. There...
08/17/2022

Debiased Inference on Identified Linear Functionals of Underidentified Nuisances via Penalized Minimax Estimation

We study generic inference on identified linear functionals of nonunique...
06/16/2019

Depth-based Weighted Jackknife Empirical Likelihood for Non-smooth U-structure Equations

In many applications, parameters of interest are estimated by solving so...