Tests for Error Correlation in the Functional Linear Model

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A survey of functional principal component analysis (2014, background): “A recent paper by Gabrys et al. (2010) is an example in this direction.”
Testing the Equality of Covariance Operators in Functional Samples (2011, methodology): “point for many functional data analysis procedures, Reiss & Ogden (2007), Gervini (2008), Yao & Müller (2010), Gabrys et al. (2010) are just a handful of illustrative references. The FPC’s are the eigenfunctions of the covariance operator. This paper focuses on testing if the covariance operators of”
Estimation of the mean of functional time series and a two‐sample problem (2011, methodology): “We consider a stationary functional time series {"i.t/, i ∈ Z, t ∈ [0, 1]}, which we can view as an error sequence in a more complex functional model, e.g. a regression model, as in Gabrys et al. (2010).”
Asymptotic normality of the principal components of functional time series (2013, methodology): “We focused on L4-m-approximability because it has already been used in the functional context, in addition to Hörmann and Kokoszka [17]; see also [12,20].”
Testing stationarity of functional time series (2014, methodology): “For example, Lee and Schmidt (1996) and Giraitis et al. (2003) used it to detect long memory, with short memory as the null hypothesis.”