Optimal minimax rates against nonsmooth alternatives
Optimal minimax rates against nonsmooth alternatives
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针对非光滑替代方案的最优极小极大率
DOI：
10.1093/ectj/utab030
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Nishiyama Yoshihiko
中科院分区：
文献类型：
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作者：
Hitomi Kohtaro;Iwasawa Masamune;Nishiyama Yoshihiko
这项研究调查了当另一种假设建立在一组非光滑函数上时，规格检验的最优极小极大比率。该集合由有界函数组成，这些函数不一定是可微的，导数没有光滑性约束。在误差方差结构未知的工具变量回归模型中，我们发现最优极小极大率为，其中为样本量。这一比率是通过基于非参数和参数方差估计之间的差异的简单检验来实现的。仿真研究表明，该测试对各种非光滑方案具有较好的效果。对恩格尔曲线规范的实证应用强调了该检验的良好适用性。
This study investigates optimal minimax rates for specification testing when the alternative hypothesis is built on a set of nonsmooth functions. The set consists of bounded functions that are not necessarily differentiable with no smoothness constraints imposed on their derivatives. In the instrumental variable regression set up with an unknown error variance structure, we find that the optimal minimax rate is, wherenis the sample size. The rate is achieved by a simple test based on the difference between nonparametric and parametric variance estimators. Simulation studies illustrate that the test has reasonable power against various nonsmooth alternatives. The empirical application to Engel curves specification emphasizes the good applicability of the test.