Journal
STAT
Volume 10, Issue 1, Pages -Publisher
WILEY
DOI: 10.1002/sta4.390
Keywords
functional data; penalized regression; robust procedures
Categories
Funding
- National Natural Science Foundation of China [11971001]
- Natural Science Foundation of Beijing Municipality [1182002]
- Natural Sciences and Engineering Research Council of Canada (NSERC) [2018-06008]
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The paper introduces a robust method for function-on-function linear regression using M-estimation and penalized spline regression, which is able to handle atypical observations effectively. Through several simulation studies and two real data examples, the efficiency and performance of the proposed method are demonstrated.
Function-on-function linear regression is an essential tool in characterizing the linear relationship between a functional response and a functional predictor. However, most of the estimation methods for this model are based on the least-squares procedure, which is sensitive to atypical observations. In this paper, we present a robust method for the function-on-function linear model using M-estimation and penalized spline regression. A fast iterative algorithm is provided to compute the estimates. The efficiency of the proposed robust penalized M-estimator is investigated with several simulation studies in comparison with the conventional method. We demonstrate the performance of the proposed robust method with two real data examples in a capital bike-sharing study and a Hawaii ocean time-series program.
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