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Full-Text Articles in Social and Behavioral Sciences
Estimation Of Nonparametric Conditional Moment Models With Possibly Nonsmooth Moments, Xiaohong Chen, Demian Pouzo
Estimation Of Nonparametric Conditional Moment Models With Possibly Nonsmooth Moments, Xiaohong Chen, Demian Pouzo
Cowles Foundation Discussion Papers
This paper studies nonparametric estimation of conditional moment models in which the residual functions could be nonsmooth with respect to the unknown functions of endogenous variables. It is a problem of nonparametric nonlinear instrumental variables (IV) estimation, and a difficult nonlinear ill-posed inverse problem with an unknown operator. We first propose a penalized sieve minimum distance (SMD) estimator of the unknown functions that are identified via the conditional moment models. We then establish its consistency and convergence rate (in strong metric), allowing for possibly non-compact function parameter spaces, possibly non-compact finite or infinite dimensional sieves with flexible lower semicompact or …
Estimation Of Nonparametric Conditional Moment Models With Possibly Nonsmooth Generalized Residuals, Xiaohong Chen, Demian Pouzo
Estimation Of Nonparametric Conditional Moment Models With Possibly Nonsmooth Generalized Residuals, Xiaohong Chen, Demian Pouzo
Cowles Foundation Discussion Papers
This paper studies nonparametric estimation of conditional moment models in which the generalized residual functions can be nonsmooth in the unknown functions of endogenous variables. This is a nonparametric nonlinear instrumental variables (IV) problem. We propose a class of penalized sieve minimum distance (PSMD) estimators which are minimizers of a penalized empirical minimum distance criterion over a collection of sieve spaces that are dense in the infinite dimensional function parameter space. Some of the PSMD procedures use slowly growing finite dimensional sieves with flexible penalties or without any penalty; some use large dimensional sieves with lower semicompact and/or convex penalties. …
Estimation Of Nonparametric Conditional Moment Models With Possibly Nonsmooth Generalized Residuals, Xiaohong Chen, Demian Pouzo
Estimation Of Nonparametric Conditional Moment Models With Possibly Nonsmooth Generalized Residuals, Xiaohong Chen, Demian Pouzo
Cowles Foundation Discussion Papers
This paper studies nonparametric estimation of conditional moment restrictions in which the generalized residual functions can be nonsmooth in the unknown functions of endogenous variables. This is a nonparametric nonlinear instrumental variables (IV) problem. We propose a class of penalized sieve minimum distance (PSMD) estimators, which are minimizers of a penalized empirical minimum distance criterion over a collection of sieve spaces that are dense in the infinite dimensional function parameter space. Some of the PSMD procedures use slowly growing finite dimensional sieves with flexible penalties or without any penalty; others use large dimensional sieves with lower semicompact and/or convex penalties. …
Efficient Estimation Of Semiparametric Conditional Moment Models With Possibly Nonsmooth Residuals, Xiaohong Chen, Demian Pouzo
Efficient Estimation Of Semiparametric Conditional Moment Models With Possibly Nonsmooth Residuals, Xiaohong Chen, Demian Pouzo
Cowles Foundation Discussion Papers
This paper considers semiparametric efficient estimation of conditional moment models with possibly nonsmooth residuals in unknown parametric components ( theta ) and unknown functions ( h ) of endogenous variables. We show that: (1) the penalized sieve minimum distance (PSMD) estimator ( theta\hat,h\hat ) can simultaneously achieve root- n asymptotic normality of theta\hat and nonparametric optimal convergence rate of h\hat , allowing for noncompact function parameter spaces; (2) a simple weighted bootstrap procedure consistently estimates the limiting distribution of the PSMD theta\hat ; (3) the semiparametric efficiency bound formula of Ai and Chen (2003) remains valid for conditional models with …
Efficient Estimation Of Semiparametric Conditional Moment Models With Possibly Nonsmooth Residuals, Xiaohong Chen, Demian Pouzo
Efficient Estimation Of Semiparametric Conditional Moment Models With Possibly Nonsmooth Residuals, Xiaohong Chen, Demian Pouzo
Cowles Foundation Discussion Papers
For semi/nonparametric conditional moment models containing unknown parametric components (theta) and unknown functions of endogenous variables (h), Newey and Powell (2003) and Ai and Chen (2003) propose sieve minimum distance (SMD) estimation of (theta, h) and derive the large sample properties. This paper greatly extends their results by establishing the followings: (1) The penalized SMD (PSMD) estimator (hat{theta}, hat{h}) can simultaneously achieve root- n asymptotic normality of theta hat and nonparametric optimal convergence rate of hat{h}, allowing for models with possibly nonsmooth residuals and/or noncompact infinite dimensional parameter spaces. (2) A simple weighted bootstrap procedure can consistently estimate the limiting …