Optimal testing for additivity in multiple nonparametric regression
Optimal testing for additivity in multiple nonparametric regression
复制标题
多重非参数回归中可加性的最佳测试
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
T. Sapatinas
中科院分区：
文献类型：
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作者：
F. Abramovich;I. Feis;T. Sapatinas
考虑标准多元非参数回归模型中的可加性检验问题。我们得到了最优的（在极大极小意义下）非自适应和自适应的假设检验程序，以对抗复合非参数替代方案，即响应函数包含在L2（[0，1]d）-范数中与零分离的二阶或更高阶的相互作用，并且还具有一些光滑性质。为了阐明所获得的理论结果，我们进行了广泛的模拟研究，以检查有限样本的性能所提出的假设检验程序，并比较它们与一系列其他测试可加性在文献中。
We consider the problem of testing for additivity in the standard multiple nonparametric regression model. We derive optimal (in the minimax sense) non- adaptive and adaptive hypothesis testing procedures for additivity against the composite nonparametric alternative that the response function involves interactions of second or higher orders separated away from zero in L2([0, 1]d)-norm and also possesses some smoothness properties. In order to shed some light on the theoretical results obtained, we carry out a wide simulation study to examine the finite sample performance of the proposed hypothesis testing procedures and compare them with a series of other tests for additivity available in the literature.