This paper introduces a novel hypothesis test for additivity in nonparametric regression models. Inspired by recent advances in the asymptotic theory of analysis of variance when the number of factor levels is large, we develop a test statistic that checks for possible nonlinear relations between the available predictors and the residuals from fitting the additive model. The asymptotic distribution of the test statistic is established under the null and local alternative hypotheses, demonstrating that it can detect alternatives at the rate of . An advantage over some methods in the literature is that the proposed method maintains its level close to nominal under heteroscedasticity and can be applied to both fixed and random designs. Extensive simulations suggest that the proposed test outperforms competitors for small sample sizes, especially for fixed designs, and performs competitively for larger sample sizes. The proposed method is illustrated with a real dataset.

中文翻译：

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检验非参数异方差回归模型中的可加性

本文介绍了非参数回归模型中可加性的新假设检验。受到因子水平数较大时方差分析渐近理论的最新进展的启发，我们开发了一个检验统计量，用于检查可用预测变量与拟合加性模型的残差之间可能存在的非线性关系。检验统计量的渐近分布是在零假设和局部替代假设下建立的，证明它可以以 的速率检测替代。与文献中的一些方法相比，所提出的方法在异方差下保持其接近名义的水平，并且可以应用于固定和随机设计。广泛的模拟表明，建议的测试在小样本量方面优于竞争对手，尤其适用于固定设计，并且在较大样本量的情况下具有竞争力。所提出的方法用一个真实的数据集来说明。