2025
Prediction intervals and bands with improved coverage for functional data under noisy discrete observation
KRAUS, DavidZákladní údaje
Originální název
Prediction intervals and bands with improved coverage for functional data under noisy discrete observation
Autoři
KRAUS, David (203 Česká republika, garant, domácí)
Vydání
Journal of Applied Statistics, Taylor and Francis Ltd. 2025, 0266-4763
Další údaje
Jazyk
angličtina
Typ výsledku
Článek v odborném periodiku
Obor
10103 Statistics and probability
Stát vydavatele
Velká Británie a Severní Irsko
Utajení
není předmětem státního či obchodního tajemství
Odkazy
Impakt faktor
Impact factor: 1.200 v roce 2023
Organizační jednotka
Přírodovědecká fakulta
UT WoS
001343886300001
EID Scopus
2-s2.0-85207935495
Klíčová slova anglicky
Coverage; curve reconstruction; functional data analysis; noisy discrete observation; prediction set; spline smoothing
Štítky
Příznaky
Mezinárodní význam, Recenzováno
Změněno: 20. 5. 2025 12:58, Mgr. Marie Novosadová Šípková, DiS.
Anotace
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.