期刊
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
卷 107, 期 500, 页码 1599-1609出版社
AMER STATISTICAL ASSOC
DOI: 10.1080/01621459.2012.734196
关键词
Asymptotics; Functional data analysis; Functional principal components; Hierarchical model; Lifetable; Longitudinal data; Mortality; Rate of convergence; Repeated measures; Uniform convergence
资金
- NSF [DMS08-0619, DMS11-04426]
- Direct For Mathematical & Physical Scien [1104426] Funding Source: National Science Foundation
- Division Of Mathematical Sciences [1104426] Funding Source: National Science Foundation
We introduce a new methodological framework for repeatedly observed and thus dependent functional data, alining at situations where curves are recorded repeatedly for each subject in a sample. Our methodology covers, the case where the recordings of the curves are scheduled on a regular and dense grid and also situations more typical for longitudinal studies, where the timing of recordings is often sparse and random. The proposed models lead to an interpretable and straightforward decomposition of the inherent variation in repeatedly observed functional data and are implemented through a straightforward two-step functional principal component analysis. We provide consistency results and asymptotic convergence rates for the estimated model components. We compare the proposed model with an alternative approach via a two-dimensional Karhunen-Loeve expansion and illustrate it through the analysis of longitudinal mortality data from period lifetables that are repeatedly observed for a sample of countries over many years, and also through simulation studies. This article has online supplementary materials.
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