论文标题
使用空间符号进行无限尺寸数据的多样本比较
Multi-sample Comparison Using Spatial Signs for Infinite Dimensional Data
论文作者
论文摘要
我们考虑了方差类型问题的分析，其中样本观测是无限尺寸空间中的随机元素。这种情况涵盖了观测值是随机函数的情况。对于这样一个问题，我们提出了基于空间标志的测试。我们开发了渐近实现以及自举实现以及该测试的排列实施，并研究了它们的大小和功率属性。我们将测试的性能与文献中研究的功能数据方差分析的几种基于平均值的测试进行了比较。有趣的是，我们的测试不仅在具有沉重的尾巴或偏斜分布的几种非高斯模型中胜过平均测试，而且在某些高斯模型中。此外，我们还将测试的性能与涉及受污染概率分布的几种模型中的平均测试进行了比较。最后，我们在三个真实数据集中证明了这些测试的性能：加拿大天气数据集，肉类样品化学分析的光谱数据集以及志愿者的矫形器测量数据集。
We consider an analysis of variance type problem, where the sample observations are random elements in an infinite dimensional space. This scenario covers the case, where the observations are random functions. For such a problem, we propose a test based on spatial signs. We develop an asymptotic implementation as well as a bootstrap implementation and a permutation implementation of this test and investigate their size and power properties. We compare the performance of our test with that of several mean based tests of analysis of variance for functional data studied in the literature. Interestingly, our test not only outperforms the mean based tests in several non-Gaussian models with heavy tails or skewed distributions, but in some Gaussian models also. Further, we also compare the performance of our test with the mean based tests in several models involving contaminated probability distributions. Finally, we demonstrate the performance of these tests in three real datasets: a Canadian weather dataset, a spectrometric dataset on chemical analysis of meat samples and a dataset on orthotic measurements on volunteers.
