Components and completion of partially observed functional data

KRAUS, David. Components and completion of partially observed functional data. Journal of the Royal Statistical Society: Series B (Statistical Methodology). London: Blackwell Publishing., 2015, vol. 77, No 4, p. 777-801. ISSN 1369-7412. Available from: https://dx.doi.org/10.1111/rssb.12087.

Basic information

• Original name: Components and completion of partially observed functional data
• Authors: KRAUS, David.
• Edition: Journal of the Royal Statistical Society: Series B (Statistical Methodology), London, Blackwell Publishing. 2015, 1369-7412.

Other information

• Original language: English
• Type of outcome: Article in a journal
• Confidentiality degree: is not subject to a state or trade secret
• WWW: URL
• Impact factor: Impact factor: 4.222
• Doi: http://dx.doi.org/10.1111/rssb.12087
• UT WoS: 000358608300003
• Keywords in English: Functional data analysis; Incomplete observation; Inverse problem; Prediction; Principal component analysis; Regularization
• Tags: International impact, Reviewed

Abstract

Functional data are traditionally assumed to be observed on the same domain. Motivated by a data set of heart rate temporal profiles, we develop methodology for the analysis of incomplete functional samples where each curve may be observed on a subset of the domain and unobserved elsewhere. We formalize this observation regime and develop the fundamental procedures of functional data analysis for this framework: estimation of parameters (mean and covariance operator) and principal component analysis. Principal scores of a partially observed function cannot be computed directly and we solve this challenging issue by estimating their best predictions as linear functionals of the observed part of the trajectory. Next, we propose a functional completion procedure that recovers the missing part by using the observed part of the curve. We construct prediction intervals for principal scores and bands for missing parts of trajectories. The prediction problems are seen to be ill-posed inverse problems; regularization techniques are used to obtain a stable solution. A simulation study shows the good performance of our methods. We illustrate the methods on the heart rate data and provide practical computational algorithms and theoretical arguments and proofs of all results.