Components and completion of partially observed functional data

J 2015

Components and completion of partially observed functional data

KRAUS, David

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

Language

English

Type of outcome

Article in a journal

Confidentiality degree

is not subject to a state or trade secret

References:

URL

Impact factor

Impact factor: 4.222

Marked to be transferred to RIV

DOI

https://doi.org/10.1111/rssb.12087

UT WoS

000358608300003

Keywords in English

Functional data analysis; Incomplete observation; Inverse problem; Prediction; Principal component analysis; Regularization

Abstract

In the original language

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.

Cite

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://doi.org/10.1111/rssb.12087.

@article{1323996,
   author = {Kraus, David},
   article_location = {London},
   article_number = {4},
   doi = {https://doi.org/10.1111/rssb.12087},
   keywords = {Functional data analysis; Incomplete observation; Inverse problem; Prediction; Principal component analysis; Regularization},
   language = {eng},
   issn = {1369-7412},
   journal = {Journal of the Royal Statistical Society: Series B (Statistical Methodology)},
   title = {Components and completion of partially observed functional data},
   url = {http://dx.doi.org/10.1111/rssb.12087},
   volume = {77},
   year = {2015}
}

TY  - JOUR
ID  - 1323996
AU  - Kraus, David
PY  - 2015
TI  - Components and completion of partially observed functional data
JF  - Journal of the Royal Statistical Society: Series B (Statistical Methodology)
VL  - 77
IS  - 4
SP  - 777-801
EP  - 777-801
PB  - Blackwell Publishing.
SN  - 13697412
KW  - Functional data analysis
KW  - Incomplete observation
KW  - Inverse problem
KW  - Prediction
KW  - Principal component analysis
KW  - Regularization
UR  - http://dx.doi.org/10.1111/rssb.12087
L2  - http://dx.doi.org/10.1111/rssb.12087
N2  - 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.
ER  -

KRAUS, David. Components and completion of partially observed functional data. \textit{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://doi.org/10.1111/rssb.12087.

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