### 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 language | English (US) |
---|---|

Pages (from-to) | 945-962 |

Number of pages | 18 |

Journal | Biometrika |

Volume | 105 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1 2018 |

### Fingerprint

### 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

*Biometrika*,

*105*(4), 945-962. https://doi.org/10.1093/biomet/asy041

}

*Biometrika*, vol. 105, no. 4, pp. 945-962. https://doi.org/10.1093/biomet/asy041

**Functional prediction through averaging estimated functional linear regression models.** / Zhang, Xinyu; Chiou, Jeng Min; Ma, Yanyuan.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Functional prediction through averaging estimated functional linear regression models

AU - Zhang, Xinyu

AU - Chiou, Jeng Min

AU - Ma, Yanyuan

PY - 2018/12/1

Y1 - 2018/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85058886963&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85058886963&partnerID=8YFLogxK

U2 - 10.1093/biomet/asy041

DO - 10.1093/biomet/asy041

M3 - Article

AN - SCOPUS:85058886963

VL - 105

SP - 945

EP - 962

JO - Biometrika

JF - Biometrika

SN - 0006-3444

IS - 4

ER -