Journal
JOURNAL OF MULTIVARIATE ANALYSIS
Volume 147, Issue -, Pages 218-233Publisher
ELSEVIER INC
DOI: 10.1016/j.jmva.2016.02.002
Keywords
Functional data analysis (FDA); Long-range dependence; Eigenfunctions; Eigenvalues; Scores
Categories
Funding
- German Research Foundation (DFG) through research unit [FOR 1882]
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Observations in functional data analysis (FDA) are often perturbed by random noise. In this paper we consider estimation of eigenvalues, eigenfunctions and scores for FDA models with weakly or strongly dependent error processes. As it turns out, the asymptotic distribution of estimated eigenvalues and eigenfunctions does not depend on the strength of dependence in the error process. In contrast, the rate of convergence and the asymptotic distribution of estimated scores differ distinctly between the cases of short and long memory. Simulations illustrate the asymptotic results. (C) 2016 Elsevier Inc. All rights reserved.
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