A significance test for covariates in nonparametric regression

作者：Lavergne Pascal^*; Maistre Samuel; Patilea Valentin

来源：Electronic Journal of Statistics, 2015, 9(1): 643-678.

DOI：10.1214/15-EJS1005

• Asymptotic pivotal test statistic
• bootstrap
• kernel smoothing
• U-statistic

We consider testing the significance of a subset of covariates in a nonparametric regression. These covariates can he continuous and/or discrete. We propose a new kernel-based test that smoothes only over the covariates appearing under the null hypothesis, so that the curse of dimensionality is mitigated. The test statistic is asymptotically pivotal and the rate of which the test detects local alternatives depends only on the dimension of the covariates under the null hypothesis. We show the validity of wild bootstrap for the test. In small samples, our test is competitive compared to existing procedures.

• 出版日期2015