Simulation of warping processes with applications to temperature data
Abstract
Curve registration plays a major role in functional data analysis by separating amplitude and phase variation through warping functions and the accurate simulation of warping processes is essential for developing statistical methods that properly account for phase variability in functional data. In this paper, we focus on the simulation of continuous warping processes with a prescribed expectation and a controllable variance. We study and compare three procedures, including two existing methods and a new algorithm based on randomized empirical cumulative distribution functions. For each approach, we provide an operational description and establish theoretical results for the first two moments of the simulated processes. A numerical study illustrates the theoretical findings and highlights the respective merits of the three methods. Finally, we present an application to the analysis of hourly temperature data spatially averaged over Canada, based on simulated realizations from a warping process estimated using spatially averaged temperature quantile functions.
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BibTeX
@misc{mehaute2026simulation,
title = {{Simulation of warping processes with applications to temperature data}},
author = {Nolwenn Le Méhauté and Jean-François Coeurjolly and Marie-Hélène Descary},
howpublished = {HAL},
year = {2026},
month = oct,
eprint = {2601.02154},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05427982v2},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Simulation of warping processes with applications to temperature data
AU - Nolwenn Le Méhauté
AU - Jean-François Coeurjolly
AU - Marie-Hélène Descary
PY - 2026
DA - 2026/10/21
PB - HAL
UR - https://hal.science/hal-05427982v2
AB - Curve registration plays a major role in functional data analysis by separating amplitude and phase variation through warping functions and the accurate simulation of warping processes is essential for developing statistical methods that properly account for phase variability in functional data. In this paper, we focus on the simulation of continuous warping processes with a prescribed expectation and a controllable variance. We study and compare three procedures, including two existing methods and a new algorithm based on randomized empirical cumulative distribution functions. For each approach, we provide an operational description and establish theoretical results for the first two moments of the simulated processes. A numerical study illustrates the theoretical findings and highlights the respective merits of the three methods. Finally, we present an application to the analysis of hourly temperature data spatially averaged over Canada, based on simulated realizations from a warping process estimated using spatially averaged temperature quantile functions.
ER -