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Time-Varying Additive Models for Longitudinal Data
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DOI：10.1080/01621459.2013.778776.png)
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The additive model is an effective dimension-reduction approach that also provides flexibility in modeling the relation between a response variable and key covariates. The literature is largely developed to scalar response and vector covariates. In this article, more complex data are of interest, where both the response and the covariates are functions. We propose a functional additive model together with a new backfitting algorithm to estimate the unknown regression functions, whose components are time-dependent additive functions of the covariates. Such functional data may not be completely observed since measurements may only be collected intermittently at discrete time points. We develop a unified platform and an efficient approach that can cover both dense and sparse functional data and the needed theory for statistical inference. We also establish the oracle properties of the proposed estimators of the component functions.
Keyword:
Functional data
Local linear smoothing
Oracle property
Smooth backfitting
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被引数:
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UNIFORM CONVERGENCE RATES FOR NONPARAMETRIC REGRESSION AND PRINCIPAL COMPONENT ANALYSIS IN FUNCTIONAL/LONGITUDINAL DATA函数/纵向数据中非参数回归和主成分分析的统一收敛速度.png)
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