Tests of Normality of Functional Data
Tests of Normality of Functional Data
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DOI：
10.1111/insr.12362
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发表时间：
2020-02-17
影响因子：
2
通讯作者：
Kokoszka, Piotr
中科院分区：
文献类型：
--
作者：
Gorecki, Tomasz;Horvath, Lajos;Kokoszka, Piotr
本文涉及测试从函数回归模型估计的曲线和误差曲线样本的正态性。我们提出了一种基于将多元正态性检验应用于函数主成分分数向量的通用范例。我们检查许多此类测试的有限样本性能，并选择性能最佳的测试。我们将它们应用于几个广泛使用的功能数据集，并确定哪些可以被视为正常数据，可能在适当的转换之后。我们还为我们研究的所有测试的软件实现提供实用指导，并根据函数主成分分数的样本偏度和峰度为测试开发大样本论证。
The paper is concerned with testing normality in samples of curves and error curves estimated from functional regression models. We propose a general paradigm based on the application of multivariate normality tests to vectors of functional principal components scores. We examine finite sample performance of a number of such tests and select the best performing tests. We apply them to several extensively used functional data sets and determine which can be treated as normal, possibly after a suitable transformation. We also offer practical guidance on software implementations of all tests we study and develop large sample justification for tests based on sample skewness and kurtosis of functional principal component scores.