Two-sample tests in functional data analysis starting from discrete data

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Testing relevant hypotheses in functional time series via self‐normalization (2018, methodology): “For testing either of the hypotheses, we propose to first estimate the multiple change points by adapting one of the commonly used methods such as binary segmentation or wild binary segmentation [see for example Vostrikova (1981); Harchaoui and Lévy-Leduc (2010); Fryzlewicz (2014); Zhang and Lavitas”
Second-Order Comparison of Gaussian Random Functions and the Geometry of DNA Minicircles (2010, background): “Hall and Van Keilegom (2007) studied the important issue of the effect that the data smoothing step may have on two-sample testing.”
Functional data analysis in the Banach space of continuous functions (2017, background): “Hall and Van Keilegom [24] studied the effect of smoothing when converting discrete observations into functional data.”
Functional Data Analysis (2016, methodology): “Other two sample tests have been proposed for distributions of functional data (Hall & Van Keilegom 2007) and for covariance functions (Panaretos, Kraus & Maddocks 2010; Boente, Rodriguez & Sued 2011).”
Interval-wise testing for functional data (2017, methodology): “The latter approach relies instead on permutation or bootstrap computational intensive techniques (Hall and Tajvidi 2002; Cardot et al. 2007; Hall and Van Keilegom 2007).”