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Online Estimation for Functional Data
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DOI：10.1080/01621459.2021.2002158.png)
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Abstract
En 中文
Functional data analysis has attracted considerable interest and is facing new challenges, one of which is the increasingly available data in a streaming manner. In this article we develop an online nonparametric method to dynamically update the estimates of mean and covariance functions for functional data. The kernel-type estimates can be decomposed into two sufficient statistics depending on the data-driven bandwidths. We propose to approximate the future optimal bandwidths by a sequence of dynamically changing candidates and combine the corresponding statistics across blocks to form the updated estimation. The proposed online method is easy to compute based on the stored sufficient statistics and the current data block. We derive the asymptotic normality and, more importantly, the relative efficiency lower bounds of the online estimates of mean and covariance functions. This provides insight into the relationship between estimation accuracy and computational cost driven by the length of candidate bandwidth sequence. Simulations and real data examples are provided to support such findings. Supplementary materials for this article are available online.
Keywords:
Dynamic candidate bandwidths
Online learning
Relative efficiency
Streaming data
Journal
J
IF:
3
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5.2K
Citations:
4.8W
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UNIFORM CONVERGENCE RATES FOR NONPARAMETRIC REGRESSION AND PRINCIPAL COMPONENT ANALYSIS IN FUNCTIONAL/LONGITUDINAL DATA.png)
ANNALS OF STATISTICS
OAAI
ANNALS OF STATISTICSIF3.7
OAAIShareSaveShareSaveShareSaveCONSISTENCY OF RESTRICTED MAXIMUM LIKELIHOOD ESTIMATORS OF PRINCIPAL COMPONENTSANNALS OF STATISTICSOAAI
ANNALS OF STATISTICSIF3.7
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