期刊
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
卷 110, 期 510, 页码 824-836出版社
AMER STATISTICAL ASSOC
DOI: 10.1080/01621459.2014.931859
关键词
Error-in-variables; Functional regression; Index model; Nonlinear regression; Sparsely sampled functional data
资金
- NSF [DMS-1209057]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1209057] Funding Source: National Science Foundation
The regression problem involving functional predictors has many important applications and a number of functional regression methods have been developed. However, a common complication in functional data analysis is one of sparsely observed curves, that is predictors that are observed, with error, on a small subset of the possible time points. Such sparsely observed data induce an errors-in-variables model, where one must account for measurement error in the functional predictors. Faced with sparsely observed data, most current functional regression methods simply estimate the unobserved predictors and treat them as fully observed; thus failing to account for the extra uncertainty from the measurement error. We propose a new functional errors-in-variables approach, sparse index model functional estimation (SIMFE), which uses a functional index model formulation to deal with sparsely observed predictors. SIMFE has several advantages over more traditional methods. First, the index model implements a nonlinear regression and uses an accurate supervised method to estimate the lower dimensional space into which the predictors should be projected. Second, SEMFE can be applied to both scalar and functional responses and multiple predictors. Finally, SIIMFE uses a mixed effects model to effectively deal with very sparsely observed functional predictors and to correctly model the measurement error. Supplementary materials for this article are available online.
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