Robust Global Testing for Mean Functions in Sparse and Dense Functional and Longitudinal Data
Abstract
We develop a robust quadratic score test for a specified mean function in functional and longitudinal data. The construction combines a convex loss with subject-level scores while retaining dependence among repeated measurements. An explicit score-centering condition ensures that the target remains the population mean. We establish the null distribution and Sobolev separation rates under sparse and dense sampling, identifying a transition from a nonparametric testing rate to the root-n boundary. A Gaussian multiplier bootstrap remains valid across these regimes, including settings with non-Gaussian quadratic limits. For implementation, we use a finite spline approximation and estimate the curvature through symmetric score increments. Under the stated conditions, the feasible procedure preserves null calibration and attains a consistency separation rate matching the lower bound over model classes containing a Gaussian submodel. Simulations illustrate the performance of squared, Huber, and absolute losses under regular errors and contamination, and an analysis of longitudinal CD4 counts demonstrates the method.
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BibTeX
@misc{mostafaiy2026robust,
title = {{Robust Global Testing for Mean Functions in Sparse and Dense Functional and Longitudinal Data}},
author = {Behdad Mostafaiy and Mustafa Abduljabbar Dawood},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38307},
eprint = {2610.38307},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38307},
}
RIS
TY - UNPB
TI - Robust Global Testing for Mean Functions in Sparse and Dense Functional and Longitudinal Data
AU - Behdad Mostafaiy
AU - Mustafa Abduljabbar Dawood
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38307
UR - https://arxiv.org/abs/2610.38307
AB - We develop a robust quadratic score test for a specified mean function in functional and longitudinal data. The construction combines a convex loss with subject-level scores while retaining dependence among repeated measurements. An explicit score-centering condition ensures that the target remains the population mean. We establish the null distribution and Sobolev separation rates under sparse and dense sampling, identifying a transition from a nonparametric testing rate to the root-n boundary. A Gaussian multiplier bootstrap remains valid across these regimes, including settings with non-Gaussian quadratic limits. For implementation, we use a finite spline approximation and estimate the curvature through symmetric score increments. Under the stated conditions, the feasible procedure preserves null calibration and attains a consistency separation rate matching the lower bound over model classes containing a Gaussian submodel. Simulations illustrate the performance of squared, Huber, and absolute losses under regular errors and contamination, and an analysis of longitudinal CD4 counts demonstrates the method.
ER -