Functional prediction through averaging estimated functional linear regression models

doi:10.1093/biomet/asy041

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	Functional prediction through averaging estimated functional linear regression models
	Zhang, Xinyu1 ; Chiou, Jeng-Min 2; Ma, Yanyuan 3
	2018-12-01
发表期刊	BIOMETRIKA
ISSN	0006-3444
卷号	105 期号:4 页码:945-962
摘要	Prediction is often the primary goal of data analysis. In this work, we propose a novel model averaging approach to the prediction of a functional response variable. We develop a crossvalidation model averaging estimator based on functional linear regression models in which the response and the covariate are both treated as random functions. We show that the weights chosen by the method are asymptotically optimal in the sense that the squared error loss of the predicted function is as small as that of the infeasible best possible averaged function. When the true regression relationship belongs to the set of candidate functional linear regression models, the averaged estimator converges to the true model and can estimate the regression parameter functions at the same rate as under the true model. Monte Carlo studies and a data example indicate that in most cases the approach performs better than model selection.
关键词	Asymptotic optimality Crossvalidation Functional data Model averaging Weighting
DOI	10.1093/biomet/asy041
语种	英语
资助项目	National Natural Science Foundation of China ; U.S. National Science Foundation ; U.S. National Institute of Neurological Disorders and Strokes ; Academia Sinica of Taiwan ; Ministry of Science and Technology of Taiwan
WOS研究方向	Life Sciences & Biomedicine - Other Topics ; Mathematical & Computational Biology ; Mathematics
WOS类目	Biology ; Mathematical & Computational Biology ; Statistics & Probability
WOS记录号	WOS:000452741300014
出版者	OXFORD UNIV PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/32045
专题	系统科学研究所
通讯作者	Zhang, Xinyu
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, 52 Sanlihe Rd, Beijing 100190, Peoples R China 2.Acad Sinica, Inst Stat Sci, 128 Acad Rd, Taipei 11529, Taiwan 3.Penn State Univ, Dept Stat, University Pk, PA 16802 USA
推荐引用方式 GB/T 7714	Zhang, Xinyu,Chiou, Jeng-Min,Ma, Yanyuan. Functional prediction through averaging estimated functional linear regression models[J]. BIOMETRIKA,2018,105(4):945-962.
APA	Zhang, Xinyu,Chiou, Jeng-Min,&Ma, Yanyuan.(2018).Functional prediction through averaging estimated functional linear regression models.BIOMETRIKA,105(4),945-962.
MLA	Zhang, Xinyu,et al."Functional prediction through averaging estimated functional linear regression models".BIOMETRIKA 105.4(2018):945-962.