Dynamic modelling of sparse longitudinal data and functional snippets with stochastic differential equations

• 成果类型: Article
• 署名作者: Zhou, Yidong; Mueller, Hans-Georg
• 署名单位: University of California System; University of California Davis
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkae116
• 发表日期: 2025
• 页码: 833-849
• 关键词: CONVERGENCE-RATES; measurement error; reconstruction; covariance; regression; drift

摘要

Sparse functional/longitudinal data have attracted widespread interest due to the prevalence of such data in social and life sciences. A prominent scenario where such data are routinely encountered are accelerated longitudinal studies, where subjects are enrolled in the study at a random time and are only tracked for a short amount of time relative to the domain of interest. The statistical analysis of such functional snippets is challenging since information for far-off-diagonal regions of the covariance structure is missing. Our main methodological contribution is to address this challenge by bypassing covariance estimation and instead modelling the underlying process as the solution of a data-adaptive stochastic differential equation. Taking advantage of the interface between Gaussian functional data and stochastic differential equations makes it possible to efficiently reconstruct the target process by estimating its dynamic distribution. The proposed approach allows one to consistently recover forward sample paths from functional snippets at the subject level. We establish the existence and uniqueness of the solution to the proposed data-driven stochastic differential equation and derive rates of convergence for the corresponding estimators. The finite sample performance is demonstrated with simulation studies and functional snippets arising from a growth study and spinal bone mineral density data.