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.

中文翻译：

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功能数据的正态性检验

本文涉及从功能回归模型估计的曲线和误差曲线样本中测试正态性。我们基于将多元正态性检验应用于功能性主成分评分向量的方法，提出了一种通用范例。我们检查了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，并确定可能经过适当转换后可以将其视为正常数据集。我们还为所研究的所有测试的软件实现提供实用指南，并根据功能性主成分评分的样本偏度和峰度对测试进行大样本证明。