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非参数工具变量回归非线性泛函的最优上确界范数速率与一致推断AI 解读

This paper makes several important contributions to the literature about nonparametric instrumental variables (NPIV) estimation and inference on a structural function $h_0$ and its functionals. First, we derive sup-norm convergence rates for computationally simple sieve NPIV (series 2SLS) estimators of $h_0$ and its derivatives. Second, we derive a lower bound that describes the best possible (minimax) sup-norm rates of estimating $h_0$ and its derivatives, and show that the…

半参数与非参数条件矩模型的筛 Wald 和 QLR 推断AI 解读

This 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…

弱依赖与弱条件下级数估计的最优一致收敛率及渐近正态性AI 解读

We 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…

依赖数据下高维矩条件的广义经验似然AI 解读

This paper considers the maximum generalized empirical likelihood (GEL) estimation and inference on parameters identified by high dimensional moment restrictions with weakly dependent data when the dimensions of the moment restrictions and the parameters diverge along with the sample size. The consistency with rates and the asymptotic normality of the GEL estimator are obtained by properly restricting the growth rates of the dimensions of the parameters and the moment…

依赖情形下自标准化和的 Cramér 型中等偏差AI 解读

We establish a Cramér-type moderate deviation result for self-normalized sums of weakly dependent random variables, where the moment requirement is much weaker than the non-self-normalized counterpart. The range of the moderate deviation is shown to depend on the moment condition and the degree of dependence of the underlying processes. We consider two types of self-normalization: the big-block-small-block scheme and the interlacing or equal-block scheme. Simulation study…

筛法非参数工具变量回归的最优一致收敛速度AI 解读

We study the problem of nonparametric regression when the regressor is endogenous, which is an important nonparametric instrumental variables (NPIV) regression in econometrics and a difficult ill-posed inverse problem with unknown operator in statistics. We first establish a general upper bound on the sup-norm (uniform) convergence rate of a sieve estimator, allowing for endogenous regressors and weakly dependent data. This result leads to the optimal sup-norm convergence…

非参数与半参数模型的局部识别AI 解读

In parametric, nonlinear structural models a classical sufficient condition for local identification, like Fisher (1966) and Rothenberg (1971), is that the vector of moment conditions is differentiable at the true parameter with full rank derivative matrix. We derive an analogous result for the nonparametric, nonlinear structural models, establishing conditions under which an infinite-dimensional analog of the full rank condition is sufficient for local identification.…

基于 Copula 的半参数马尔可夫模型的有效估计AI 解读

This paper considers the efficient estimation of copula-based semiparametric strictly stationary Markov models. These models are characterized by nonparametric invariant (one-dimensional marginal) distributions and parametric bivariate copula functions where the copulas capture temporal dependence and tail dependence of the processes. The Markov processes generated via tail dependent copulas may look highly persistent and are useful for financial and economic applications.…

使用辅助数据的 GMM 模型半参数效率AI 解读

We study semiparametric efficiency bounds and efficient estimation of parameters defined through general moment restrictions with missing data. Identification relies on auxiliary data containing information about the distribution of the missing variables conditional on proxy variables that are observed in both the primary and the auxiliary database, when such distribution is common to the two data sets. The auxiliary sample can be independent of the primary sample, or can be…

计量经济学不适定逆问题的收敛速度最优性AI 解读

In this paper, we clarify the relations between the existing sets of regularity conditions for convergence rates of nonparametric indirect regression (NPIR) and nonparametric instrumental variables (NPIV) regression models. We establish minimax risk lower bounds in mean integrated squared error loss for the NPIR and the NPIV models under two basic regularity conditions that allow for both mildly ill-posed and severely ill-posed cases. We show that both a simple projection…