Locally Adaptive Online Functional Data Analysis

Valentin Patilea and Jeffrey Racine

Department of Economics Working Papers from McMaster University

Abstract: We consider the problem of building adaptive, rate optimal estimators for the mean and covariance functions of random curves in the context of streaming data. In general, functional data analysis requires nonparametric smoothing of curves observed at a discrete set of design points, which may be measured with error. However, classical nonparametric smoothing methods (e.g., kernels, splines, etc.) assume that the degree of smoothness is known. In many applications functional data could be irregular, even perhaps nowhere differentiable. Moreover, the (ir)regularity of the curves could vary across their domain. We contribute to the literature by providing estimators and inference procedures that use an iterative plug-in estimator of ‘local regularity’ which delivers a computationally attractive, recursive, online updating method that is well-suited to streaming data. Theoretical support and Monte Carlo simulation evidence is provided, and code in the R language is available for the interested reader.

Keywords: Adaptive estimator; Covariance function; Hölder exponent; Optimal smoothing (search for similar items in EconPapers)
JEL-codes: C15 C21 C23 (search for similar items in EconPapers)
Pages: 98 pages
Date: 2024-06
New Economics Papers: this item is included in nep-ecm
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Persistent link: https://EconPapers.repec.org/RePEc:mcm:deptwp:2024-04

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