SSRN Author: Xiaohong ChenXiaohong Chen SSRN Content
http://www.ssrn.com/author=30333
http://www.ssrn.com/rss/en-usWed, 15 Jul 2015 01:51:33 GMTeditor@ssrn.com (Editor)Wed, 15 Jul 2015 01:51:33 GMTwebmaster@ssrn.com (WebMaster)SSRN RSS Generator 1.0New: Sieve Semiparametric Two-Step GMM Under Weak DependenceThis paper considers semiparametric two-step GMM estimation and inference with weakly dependent data, where unknown nuisance functions are estimated via sieve extremum estimation in the first step. We show that although the asymptotic variance of the second-step GMM estimator may not have a closed form expression, it can be well approximated by sieve variances that have simple closed form expressions. We present consistent or robust variance estimation, Wald tests and Hansen's (1982) over-identification tests for the second step GMM that properly reflect the first-step estimated functions and the weak dependence of the data. Our sieve semiparametric two-step GMM inference procedures are shown to be numerically equivalent to the ones computed as if the first step were parametric. A new consistent random-perturbation estimator of the derivative of the expectation of the non-smooth moment function is also provided.
http://www.ssrn.com/abstract=2630224
http://www.ssrn.com/1411774.htmlTue, 14 Jul 2015 07:12:02 GMTNew: Overidentification in Regular ModelsIn models defined by unconditional moment restrictions, specification tests are possible and estimators can be ranked in terms of efficiency whenever the number of moment restrictions exceeds the number of parameters. We show that a similar relationship between potential refutability of a model and semiparametric efficiency is present in a much broader class of settings. Formally, we show a condition we name local overidentification is required for both specification tests to have power against local alternatives and for the existence of both efficient and inefficient estimators of regular parameters. Our results immediately imply semiparametric conditional moment restriction models are typically locally overidentified, and hence their proper specification is locally testable. We further study nonparametric conditional moment restriction models and obtain a simple characterization of local overidentification in that context. As a result, we are able to determine when nonparametric ...
http://www.ssrn.com/abstract=2597670
http://www.ssrn.com/1391652.htmlThu, 23 Apr 2015 10:19:52 GMTNew: Optimal Sup-Norm Rates, Adaptivity and Inference in Nonparametric Instrumental Variables EstimationThis paper makes several contributions to the literature on the important yet difficult problem of estimating functions nonparametrically using instrumental variables. First, we derive the minimax optimal sup-norm convergence rates for nonparametric instrumental variables (NPIV) estimation of the structural function h_0 and its derivatives. Second, we show that a computationally simple sieve NPIV estimator can attain the optimal sup-norm rates for h_0 and its derivatives when h_0 is approximated via a spline or wavelet sieve. Our optimal sup-norm rates surprisingly coincide with the optimal L^2-norm rates for severely ill-posed problems, and are only up to a [log(n)]^epsilon (with epsilon < 1/2) factor slower than the optimal L^2-norm rates for mildly ill-posed problems. Third, we introduce a novel data-driven procedure for choosing the sieve dimension optimally. Our data-driven procedure is sup-norm rate-adaptive: the resulting estimator of h_0 and its derivatives converge at their ...
http://www.ssrn.com/abstract=2588495
http://www.ssrn.com/1386849.htmlThu, 02 Apr 2015 20:42:51 GMTREVISION: Sieve Wald and QLR Inferences on Semi/Nonparametric Conditional Moment ModelsThis 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 ...
http://www.ssrn.com/abstract=2518456
http://www.ssrn.com/1382613.htmlFri, 20 Mar 2015 02:03:34 GMTREVISION: Optimal Uniform Convergence Rates and Asymptotic Normality for Series Estimators Under Weak Dependence and Weak ConditionsWe show that spline and wavelet series regression estimators for weakly dependent regressors attain the optimal uniform (i.e., sup-norm) convergence rate (n/log n)^{-p/(2p d)} of Stone (1982), where d is the number of regressors and p is the smoothness of the regression function. The optimal rate is achieved even for heavy-tailed martingale difference errors with finite (2 (d/p))th absolute moment for d/p < 2. We also establish the asymptotic normality of t statistics for possibly nonlinear, irregular functionals of the conditional mean function under weak conditions. The results are proved by deriving a new exponential inequality for sums of weakly dependent random matrices, which is of independent interest.
http://www.ssrn.com/abstract=2541735
http://www.ssrn.com/1380711.htmlFri, 13 Mar 2015 10:28:59 GMTREVISION: Optimal Uniform Convergence Rates and Asymptotic Normality for Series Estimators Under Weak Dependence and Weak ConditionsWe show that spline and wavelet series regression estimators for weakly dependent regressors attain the optimal uniform (i.e., sup-norm) convergence rate (n/log n)^{-p/(2p d)} of Stone (1982), where d is the number of regressors and p is the smoothness of the regression function. The optimal rate is achieved even for heavy-tailed martingale difference errors with finite (2 (d/p))th absolute moment for d/p < 2. We also establish the asymptotic normality of t statistics for possibly nonlinear, irregular functionals of the conditional mean function under weak conditions. The results are proved by deriving a new exponential inequality for sums of weakly dependent random matrices, which is of independent interest.
http://www.ssrn.com/abstract=2541735
http://www.ssrn.com/1380383.htmlThu, 12 Mar 2015 09:25:42 GMTREVISION: Optimal Uniform Convergence Rates and Asymptotic Normality for Series Estimators Under Weak Dependence and Weak ConditionsWe show that spline and wavelet series regression estimators for weakly dependent regressors attain the optimal uniform (i.e., sup-norm) convergence rate (n/log n)^{-p/(2p d)} of Stone (1982), where d is the number of regressors and p is the smoothness of the regression function. The optimal rate is achieved even for heavy-tailed martingale difference errors with finite (2 (d/p))th absolute moment for d/p < 2. We also establish the asymptotic normality of t statistics for possibly nonlinear, irregular functionals of the conditional mean function under weak conditions. The results are proved by deriving a new exponential inequality for sums of weakly dependent random matrices, which is of independent interest.
http://www.ssrn.com/abstract=2541735
http://www.ssrn.com/1360966.htmlTue, 23 Dec 2014 20:50:47 GMTREVISION: Sieve Wald and QLR Inferences on Semi/Nonparametric Conditional Moment ModelsThis 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 ...
http://www.ssrn.com/abstract=2518456
http://www.ssrn.com/1348630.htmlWed, 05 Nov 2014 04:00:08 GMT