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Functional data analysis with increasing number of projections

Stefan Fremdt, Lajos Horvath, Piotr Kokoszka and Josef G. Steinebach

Journal of Multivariate Analysis, 2014, vol. 124, issue C, 313-332

Abstract: Functional principal components (FPC’s) provide the most important and most extensively used tool for dimension reduction and inference for functional data. The selection of the number, d, of the FPC’s to be used in a specific procedure has attracted a fair amount of attention, and a number of reasonably effective approaches exist. Intuitively, they assume that the functional data can be sufficiently well approximated by a projection onto a finite-dimensional subspace, and the error resulting from such an approximation does not impact the conclusions. This has been shown to be a very effective approach, but it is desirable to understand the behavior of many inferential procedures by considering the projections on subspaces spanned by an increasing number of the FPC’s. Such an approach reflects more fully the infinite-dimensional nature of functional data, and allows to derive procedures which are fairly insensitive to the selection of d. This is accomplished by considering limits as d→∞ with the sample size.

Keywords: Functional data; Change in mean; Increasing dimension; Normal approximation; Principal components (search for similar items in EconPapers)
Date: 2014
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