文章基本信息

标题：Dimension reduction-based significance testing in nonparametric regression
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作者：Xuehu Zhu ; Lixing Zhu
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2018
卷号：12
期号：1
页码：1468-1506
DOI：10.1214/18-EJS1414
语种：English
出版社：Institute of Mathematical Statistics
摘要：A dimension reduction-based adaptive-to-model test is proposed for significance of a subset of covariates in the context of a nonparametric regression model. Unlike existing locally smoothing significance tests, the new test behaves like a locally smoothing test as if the number of covariates was just that under the null hypothesis and it can detect local alternative hypotheses distinct from the null hypothesis at the rate that is only related to the number of covariates under the null hypothesis. Thus, the curse of dimensionality is largely alleviated when nonparametric estimation is inevitably required. In the cases where there are many insignificant covariates, the improvement of the new test is very significant over existing locally smoothing tests on the significance level maintenance and power enhancement. Simulation studies and a real data analysis are conducted to examine the finite sample performance of the proposed test.