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Modelling functional data with high-dimensional error structure. (English) Zbl 1444.62153
Aneiros, Germán (ed.) et al., Functional and high-dimensional statistics and related fields. Selected papers presented at the 5th international workshop on functional and operatorial statistics, IWFOS 2021, Brno, Czech Republic, June 23–25, 2021. Cham: Springer. Contrib. Stat., 99-106 (2020).
Summary: We propose to model raw functional data as a mixture of functions and high-dimensional error. The conventional approach to retrieve the functional component from raw data is through varied smoothing techniques. Nevertheless, smoothing itself may not be adequate when measurement error exists. We propose to use factor model to reduce the dimension of the high-dimensional measurement error, while smoothing the functional component. Our model also provides as an alternative for modelling functional data with step jump. Regularized least squares method is used to find the model estimates. We look at the asymptotic behaviour of the estimator when both the sample size and the number of points per curve go to infinity and the limiting distribution is derived.
For the entire collection see [Zbl 1446.62001].
MSC:
62R10 Functional data analysis
62E20 Asymptotic distribution theory in statistics
Software:
fda (R); KernSmooth
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References:
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