Functional prediction through averaging estimated functional linear regression models

Xinyu Zhang, Jeng Min Chiou, Yanyuan Ma

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)945-962
Number of pages18
JournalBiometrika
Volume105
Issue number4
DOIs
StatePublished - Dec 1 2018

Fingerprint

Linear Regression Model
Linear regression
Model Averaging
Averaging
Linear Models
prediction
Prediction
Regression
Squared Error Loss
Estimator
Functional Response
Random Function
Monte Carlo Study
Asymptotically Optimal
Cross-validation
Model Selection
Covariates
Data analysis
Converge
Monte Carlo method

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

Cite this

Zhang, Xinyu ; Chiou, Jeng Min ; Ma, Yanyuan. / Functional prediction through averaging estimated functional linear regression models. In: Biometrika. 2018 ; Vol. 105, No. 4. pp. 945-962.
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Functional prediction through averaging estimated functional linear regression models. / Zhang, Xinyu; Chiou, Jeng Min; Ma, Yanyuan.

In: Biometrika, Vol. 105, No. 4, 01.12.2018, p. 945-962.

Research output: Contribution to journalArticle

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