Estimation of Nonparametric Conditional Moment Models with Possibly Nonsmooth Moments
Estimation of Nonparametric Conditional Moment Models with Possibly Nonsmooth Moments
复制标题
具有可能非平滑矩的非参数条件矩模型的估计
DOI：
10.2139/ssrn.1126241
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
Demian Pouzo
中科院分区：
文献类型：
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作者：
Xiaohong Chen;Demian Pouzo
研究了残差函数相对于未知内生变量函数是非光滑的条件矩模型的非参数估计。它是一个非参数非线性工具变量估计问题，也是一个具有未知算子的非线性病态逆问题。我们首先提出了一种惩罚筛最小距离（SMD）估计器，用于通过条件矩模型识别未知函数。然后我们建立了它的一致性和收敛率（在强度量中），允许可能的非紧化函数参数空间，可能的非紧化有限或无限维筛子具有柔性的低半紧或凸惩罚，或有限维线性筛子没有惩罚。在相对低级的充分条件下，对于轻度和严重病态问题，我们证明了非线性病态逆问题的收敛速率与已知的非参数均值IV回归的极小极大最优速率一致。我们通过两个重要的应用来说明这一理论：非参数非线性IV回归的加权平均导数的插件惩罚SMD估计量的根n渐近正态性，以及非参数加性分位数IV回归的收敛速率。我们还提出了一个非参数分位数系统的模拟研究和经验估计。
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 convex penalty, or finite dimensional linear sieves without penalty. Under relatively low-level sufficient conditions, and for both mildly and severely ill-posed problems, we show that the convergence rates for the nonlinear ill-posed inverse problems coincide with the known minimax optimal rates for the nonparametric mean IV regression. We illustrate the theory by two important applications: root-n asymptotic normality of the plug-in penalized SMD estimator of a weighted average derivative of a nonparametric nonlinear IV regression, and the convergence rate of a nonparametric additive quantile IV regression. We also present a simulation study and an empirical estimation of a system of nonparametric quantile IV Engel curves.