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- Title
Adaptive estimation for functional data: Using a framelet block‐thresholding method.
- Authors
Cheng, Kun; Chen, Di‐Rong
- Abstract
This article considers a framelet block‐thresholding method for estimating mean and covariance functions from discretely sampled noisy observations. Estimated convergence rates are established for all types of sampling schemes. In particular, the results reveal a phase transition phenomenon related to the number of observations on each curve. It is shown that the proposed procedures are adaptive in automatically adjusting the smoothness properties of the underlying mean and covariance functions. In contrast, theoretical results for other smoothing methods hold in the setting where smoothness parameters are assumed to be known, since the regularization parameters of estimators that depend on smoothness properties need to be chosen carefully. Simulation studies are provided to offer empirical support for the theoretical results. A comparison with other methods demonstrates that the proposed method outperforms in adaptivity. An application to a real dataset is also provided to illustrate the proposed estimation procedure.
- Subjects
REGULARIZATION parameter; PHASE transitions; BAYES' estimation
- Publication
Canadian Journal of Statistics, 2022, Vol 50, Issue 1, p86
- ISSN
0319-5724
- Publication type
Article
- DOI
10.1002/cjs.11682