Prediction intervals and bands with improved coverage for
functional data under noisy discrete observation

J 2025

Prediction intervals and bands with improved coverage for functional data under noisy discrete observation

KRAUS, David

Basic information

Original name

Prediction intervals and bands with improved coverage for functional data under noisy discrete observation

Authors

KRAUS, David (203 Czech Republic, guarantor, belonging to the institution)

Edition

Journal of Applied Statistics, Taylor and Francis Ltd. 2025, 0266-4763

Other information

Language

English

Type of outcome

Article in a journal

Field of Study

10103 Statistics and probability

Country of publisher

United Kingdom of Great Britain and Northern Ireland

Confidentiality degree

is not subject to a state or trade secret

References:

URL

Impact factor

Impact factor: 1.200 in 2023

Organization unit

Faculty of Science

DOI

http://dx.doi.org/10.1080/02664763.2024.2420223

UT WoS

001343886300001

EID Scopus

2-s2.0-85207935495

Keywords in English

Coverage; curve reconstruction; functional data analysis; noisy discrete observation; prediction set; spline smoothing

Abstract

V originále

We revisit the classic situation in functional data analysis in which curves are observed at discrete, possibly sparse and irregular, arguments with observation noise. We focus on the reconstruction of individual curves by prediction intervals and bands. The standard approach consists of two steps: first, one estimates the mean and covariance function of curves and observation noise variance function by, e.g. penalized splines, and second, under Gaussian assumptions, one derives the conditional distribution of a curve given observed data and constructs prediction sets with required properties, usually employing sampling from the predictive distribution. This approach is well established, commonly used and theoretically valid but practically, it surprisingly fails in its key property: prediction sets constructed this way often do not have the required coverage. The actual coverage is lower than the nominal one. We investigate the cause of this issue and propose a computationally feasible remedy that leads to prediction regions with a much better coverage. Our method accounts for the uncertainty of the predictive model by sampling from the approximate distribution of its spline estimators whose covariance is estimated by a novel sandwich estimator. Our approach also applies to the important case of covariate-adjusted models.

Cite

KRAUS, David. Prediction intervals and bands with improved coverage for functional data under noisy discrete observation. Journal of Applied Statistics. Taylor and Francis Ltd., 2025, vol. 52, No 6, p. 1258-1277. ISSN 0266-4763. Available from: https://dx.doi.org/10.1080/02664763.2024.2420223.

@article{2447677,
   author = {Kraus, David},
   article_number = {6},
   doi = {http://dx.doi.org/10.1080/02664763.2024.2420223},
   keywords = {Coverage; curve reconstruction; functional data analysis; noisy discrete observation; prediction set; spline smoothing},
   language = {eng},
   issn = {0266-4763},
   journal = {Journal of Applied Statistics},
   title = {Prediction intervals and bands with improved coverage for functional data under noisy discrete observation},
   url = {https://www.tandfonline.com/doi/full/10.1080/02664763.2024.2420223},
   volume = {52},
   year = {2025}
}

TY  - JOUR
ID  - 2447677
AU  - Kraus, David
PY  - 2025
TI  - Prediction intervals and bands with improved coverage for functional data under noisy discrete observation
JF  - Journal of Applied Statistics
VL  - 52
IS  - 6
SP  - 1258-1277
EP  - 1258-1277
PB  - Taylor and Francis Ltd.
SN  - 02664763
KW  - Coverage
KW  - curve reconstruction
KW  - functional data analysis
KW  - noisy discrete observation
KW  - prediction set
KW  - spline smoothing
UR  - https://www.tandfonline.com/doi/full/10.1080/02664763.2024.2420223
N2  - We revisit the classic situation in functional data analysis in which curves are observed at discrete, possibly sparse and irregular, arguments with observation noise. We focus on the reconstruction of individual curves by prediction intervals and bands. The standard approach consists of two steps: first, one estimates the mean and covariance function of curves and observation noise variance function by, e.g. penalized splines, and second, under Gaussian assumptions, one derives the conditional distribution of a curve given observed data and constructs prediction sets with required properties, usually employing sampling from the predictive distribution. This approach is well established, commonly used and theoretically valid but practically, it surprisingly fails in its key property: prediction sets constructed this way often do not have the required coverage. The actual coverage is lower than the nominal one. We investigate the cause of this issue and propose a computationally feasible remedy that leads to prediction regions with a much better coverage. Our method accounts for the uncertainty of the predictive model by sampling from the approximate distribution of its spline estimators whose covariance is estimated by a novel sandwich estimator. Our approach also applies to the important case of covariate-adjusted models.
ER  -

KRAUS, David. Prediction intervals and bands with improved coverage for functional data under noisy discrete observation. \textit{Journal of Applied Statistics}. Taylor and Francis Ltd., 2025, vol.~52, No~6, p.~1258-1277. ISSN~0266-4763. Available from: https://dx.doi.org/10.1080/02664763.2024.2420223.

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