SSRN Author: Xiaohong ChenXiaohong Chen SSRN Content
http://www.ssrn.com/author=30333
http://www.ssrn.com/rss/en-usSun, 30 Apr 2017 01:32:00 GMTeditor@ssrn.com (Editor)Sun, 30 Apr 2017 01:32:00 GMTwebmaster@ssrn.com (WebMaster)SSRN RSS Generator 1.0REVISION: Optimal Sup-Norm Rates and Uniform Inference on Nonlinear Functionals of Nonparametric IV RegressionThis paper makes several important contributions to the literature about nonparametric instrumental variables (NPIV) estimation and inference on a structural function h<sub>0</sub> and its functionals. First, we derive sup-norm convergence rates for computationally simple sieve NPIV (series 2SLS) estimators of h<sub>0</sub> and its derivatives. Second, we derive a lower bound that describes the best possible (minimax) sup-norm rates of estimating h<sub>0</sub> and its derivatives, and show that the sieve NPIV estimator can attain the minimax rates when h<sub>0</sub> is approximated via a spline or wavelet sieve. Our optimal sup-norm rates surprisingly coincide with the optimal root-mean-squared rates for severely ill-posed problems, and are only a logarithmic factor slower than the optimal root-mean-squared rates for mildly ill-posed problems. Third, we use our sup-norm rates to establish the uniform Gaussian process strong approximations and the score bootstrap uniform confidence ...
http://www.ssrn.com/abstract=2916740
http://www.ssrn.com/1586828.htmlSat, 29 Apr 2017 08:50:32 GMTREVISION: Optimal Sup-Norm Rates and Uniform Inference on Nonlinear Functionals of Nonparametric IV RegressionThis paper makes several important contributions to the literature about nonparametric instrumental variables (NPIV) estimation and inference on a structural function h<sub>0</sub> and its functionals. First, we derive sup-norm convergence rates for computationally simple sieve NPIV (series 2SLS) estimators of h<sub>0</sub> and its derivatives. Second, we derive a lower bound that describes the best possible (minimax) sup-norm rates of estimating h<sub>0</sub> and its derivatives, and show that the sieve NPIV estimator can attain the minimax rates when h<sub>0</sub> is approximated via a spline or wavelet sieve. Our optimal sup-norm rates surprisingly coincide with the optimal root-mean-squared rates for severely ill-posed problems, and are only a logarithmic factor slower than the optimal root-mean-squared rates for mildly ill-posed problems. Third, we use our sup-norm rates to establish the uniform Gaussian process strong approximations and the score bootstrap uniform confidence ...
http://www.ssrn.com/abstract=2916740
http://www.ssrn.com/1566648.htmlWed, 15 Feb 2017 06:01:07 GMTNew: MCMC Condence Sets for Identied SetsIn complicated/nonlinear parametric models, it is generally hard to determine whether the model parameters are (globally) point identified. We provide computationally attractive procedures to construct confidence sets (CSs) for identified sets of parameters in econometric models defined through a likelihood or a vector of moments. The CSs for the identified set or for a function of the identified set (such as a subvector) are based on inverting an optimal sample criterion (such as likelihood or continuously updated GMM), where the cutoff values are computed via Monte Carlo simulations directly from a quasi posterior distribution of the criterion. We establish new Bernstein-von Mises type theorems for the posterior distributions of the quasi-likelihood ratio (QLR) and profile QLR statistics in partially identified models, allowing for singularities. These results imply that the Monte Carlo criterion-based CSs have correct frequentist coverage for the identified set as the sample size ...
http://www.ssrn.com/abstract=2805597
http://www.ssrn.com/1510698.htmlThu, 07 Jul 2016 20:59:08 GMTNew: MCMC Confidence Sets for Identified SetsIn complicated/nonlinear parametric models, it is hard to determine whether a parameter of interest is formally point identified. We provide computationally attractive procedures to construct confidence sets (CSs) for identified sets of parameters in econometric models defined through a likelihood or a vector of moments. The CSs for the identified set or for a function of the identified set (such as a subvector) are based on inverting an optimal sample criterion (such as likelihood or continuously updated GMM), where the cutoff values are computed directly from Markov Chain Monte Carlo (MCMC) simulations of a quasi posterior distribution of the criterion. We establish new Bernstein-von Mises type theorems for the posterior distributions of the quasi-likelihood ratio (QLR) and profile QLR statistics in partially identified models, allowing for singularities. These results imply that the MCMC criterion-based CSs have correct frequentist coverage for the identified set as the sample ...
http://www.ssrn.com/abstract=2775253
http://www.ssrn.com/1493998.htmlThu, 05 May 2016 12:36:35 GMT