论文标题
非参数IV模型中的自适应，最佳假设检验
Adaptive, Rate-Optimal Hypothesis Testing in Nonparametric IV Models
论文作者
论文摘要
我们提出了针对非参数仪器变量（NPIV）模型中结构函数的限制，提出了针对不平等（例如单调性，凸度）和平等（例如，参数，半参数）限制的新的自适应假设检验。我们的测试统计量基于经过修改的剩余样品类似物，该样品类似物的二级和无限制的筛子两阶段最小二乘估计器之间的二次距离。我们提供了筛分参数的计算简单，数据驱动的选择和Bonferroni调整后的卡方临界值。我们的测试适应了在未知程度的内生性和仪器强度未知的情况下替代功能的未知平滑度。它达到了$ l^{2} $中的自适应最小测试速率。也就是说，在复合null上，I型误差的最高总和和非参数替代模型的II型误差的最高措施无法通过对未知规律的NPIV模型的任何其他测试来最小化。 $ l^{2} $中的置信设置是通过反转自适应测试获得的。模拟证实，在不同的仪器和样本大小的强度上，我们的自适应测试控制大小及其有限样本功率大大超过了NPIV模型中单调性和参数限制的现有非自适应测试。提出了测试分化产品需求和恩格尔曲线的形状限制的经验应用。
We propose a new adaptive hypothesis test for inequality (e.g., monotonicity, convexity) and equality (e.g., parametric, semiparametric) restrictions on a structural function in a nonparametric instrumental variables (NPIV) model. Our test statistic is based on a modified leave-one-out sample analog of a quadratic distance between the restricted and unrestricted sieve two-stage least squares estimators. We provide computationally simple, data-driven choices of sieve tuning parameters and Bonferroni adjusted chi-squared critical values. Our test adapts to the unknown smoothness of alternative functions in the presence of unknown degree of endogeneity and unknown strength of the instruments. It attains the adaptive minimax rate of testing in $L^{2}$. That is, the sum of the supremum of type I error over the composite null and the supremum of type II error over nonparametric alternative models cannot be minimized by any other tests for NPIV models of unknown regularities. Confidence sets in $L^{2}$ are obtained by inverting the adaptive test. Simulations confirm that, across different strength of instruments and sample sizes, our adaptive test controls size and its finite-sample power greatly exceeds existing non-adaptive tests for monotonicity and parametric restrictions in NPIV models. Empirical applications to test for shape restrictions of differentiated products demand and of Engel curves are presented.
