论文标题
在功能线性回归模型中测试外生性
Testing exogeneity in the functional linear regression model
论文作者
论文摘要
我们提出了一个新型的测试统计量，用于在功能线性回归模型中测试外生性。与有限维线性回归设置中的Hausman型测试相反，无法直接扩展到功能线性回归模型。取而代之的是，我们根据功能线性回归模型中两个估计值的平方差异提出了一个测试统计量。我们在一般替代方案下得出无效和一致性下的渐近正态性。此外，我们证明了基于剩余的引导程序的引导程序一致性结果。在模拟中，我们研究了提出的测试方法的有限样本性能，并说明了基于自举的方法的优越性。特别是，相对于正则化参数的选择，引导程序方法结果更加可靠。
We propose a novel test statistic for testing exogeneity in the functional linear regression model. In contrast to Hausman-type tests in finite dimensional linear regression setups, a direct extension to the functional linear regression model is not possible. Instead, we propose a test statistic based on the sum of the squared difference of projections of the two estimators for testing the null hypothesis of exogeneity in the functional linear regression model. We derive asymptotic normality under the null and consistency under general alternatives. Moreover, we prove bootstrap consistency results for residual-based bootstraps. In simulations, we investigate the finite sample performance of the proposed testing approach and illustrate the superiority of bootstrap-based approaches. In particular, the bootstrap approaches turn out to be much more robust with respect to the choice of the regularization parameter.
