论文标题
在半功能的部分线性回归模型中测试线性性
Testing linearity in semi-functional partially linear regression models
论文作者
论文摘要
本文提出了Kolmogorov-Smirnov类型统计量和Cramér-von Mises型统计量，以测试半功能的部分线性回归模型中的线性。我们的测试统计数据基于一个由随机投影的功能协变量索引的残留标记的经验过程，该过程能够规避功能协变量带来的“维度诅咒”。在$ n^{{1/2} $ rative下，固定的替代方案和一系列局部替代方案下，提出的测试统计量的渐近性能得到了收敛。建议采用直接的野生引导程序，以估计在实际应用中进行测试所需的临界值。广泛的模拟研究的结果表明，我们的测试在有限样本中表现出色。在本文中，我们将测试应用于Tecator和AEMET数据集，以检查这些数据集的线性假设是否支持。
This paper proposes a Kolmogorov-Smirnov type statistic and a Cramér-von Mises type statistic to test linearity in semi-functional partially linear regression models. Our test statistics are based on a residual marked empirical process indexed by a randomly projected functional covariate,which is able to circumvent the "curse of dimensionality" brought by the functional covariate. The asymptotic properties of the proposed test statistics under the null, the fixed alternative, and a sequence of local alternatives converging to the null at the $n^{1/2}$ rate are established. A straightforward wild bootstrap procedure is suggested to estimate the critical values that are required to carry out the tests in practical applications. Results from an extensive simulation study show that our tests perform reasonably well in finite samples.Finally, we apply our tests to the Tecator and AEMET datasets to check whether the assumption of linearity is supported by these datasets.
