We propose a nonparametric test of significant variables in the partial derivative of a regression mean function. The derivative is estimated by local polynomial estimation and the test statistic is constructed through a variation-based measure of the derivative in the direction of variables of interest. We establish the asymptotic null distribution of the test statistic and demonstrate that it is consistent. Motivated by the null distribution, we propose a wild bootstrap test, and show that it exhibits the same null distribution, whether the null is valid or not. We perform a Monte Carlo study to demonstrate its encouraging finite sample performance. An empirical application is conducted showing how the test can be applied to infer certain aspects of regression structures in a hedonic price model.

中文翻译：

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梯度中重要变量的非参数检验

我们建议对回归均值函数的偏导数中的重要变量进行非参数检验。导数是通过局部多项式估计来估计的，而检验统计量是通过在感兴趣的变量方向上对导数进行基于变化的测量来构建的。我们建立了检验统计量的渐近零分布并证明它是一致的。受零分布的启发，我们提出了一个狂野的引导测试，并表明它表现出相同的零分布，无论零是否有效。我们进行了一项蒙特卡洛研究，以证明其令人鼓舞的有限样本性能。进行了一个实证应用，展示了如何应用该测试来推断特征价格模型中回归结构的某些方面。