Rate Optimal Specification Test When the Number of Instruments is Large
Rate Optimal Specification Test When the Number of Instruments is Large
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发表时间：
2018
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通讯作者：
K. Hitomi;Masamune Iwasawa;Y. Nishiyama
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作者：
K. Hitomi;Masamune Iwasawa;Y. Nishiyama
提出了一种基于最近邻观测的工具变量回归模型的速率最优规格检验方法。建议的测试有统一的权力对一组非光滑的替代品。对于任何维度的工具，最优的Minimax率是n-1/4，其中n是样本量。当替代由非光滑函数构造和/或仪器尺寸较大时，该速率与局部替代设置下任何测试可达到的最快可能速率一致。由于这种本地的替代品属于本研究中考虑的替代品的集合，我们的测试是更可取的，在一个大的维度设置。在模拟和实证应用与大尺寸的仪器，我们观察到，测试效果良好，功率接近一个合理的速度随着样本量的增加。
We propose a rate optimal specification test for instrumental variable regression models based on the nearest neighbor observation with respect to instruments. The proposed test has uniform power against a set of non-smooth alternatives. The optimal minimax rate is n-1/4 for any dimension of instruments, where n is sample size. This rate coincides with the fastest possible rate achievable by any tests under the local alternative setting when the alternative is constructed by a non-smooth function and/or the dimension of the instrument is large. Since such local alternative belongs to the set of alternatives considered in this study, our test is preferable in a large dimension setting. In the simulation and empirical applications with a large dimension of instruments, we observe that the test works well and the power approaches one reasonably fast as the sample size increase.