Estimation of Nonparametric Conditional Moment Models with Possibly Nonsmooth Generalized Residuals By
نویسندگان
چکیده
1 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) estima-tors, 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. We establish their consistency and the convergence rates in Banach space norms (such as a sup-norm or a root mean squared norm), allowing for possibly noncompact infinite-dimensional parameter spaces. For both mildly and severely ill-posed nonlinear inverse problems, our convergence rates in Hilbert space norms (such as a root mean squared norm) achieve the known mini-max optimal rate for the nonparametric mean IV regression. We illustrate the theory with a nonparametric additive quantile IV regression. We present a simulation study and an empirical application of estimating nonparametric quantile IV Engel curves.
منابع مشابه
Supplemental Material to ESTIMATION OF NONPARAMETRIC CONDITIONAL MOMENT MODELS WITH POSSIBLY NONSMOOTH GENERALIZED RESIDUALS BY
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