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Robust estimators of functional single index models for longitudinal data

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  • Yang Sun
  • Xiangzhong Fang

Abstract

Functional single index model is a powerful model for longitudinal data, which effectively reduces the dimension of covariates. Inspired by robust calibration of computer models, we propose a robust estimator based on Huber loss for functional single index model with fixed dimension parameter. Furthermore, we also consider the case of high dimension parameter, and proposed a robust L1 estimator of the unknown parameter based on adaptive lasso penalty. Theoretical properties including the asymptotic and non asymptotic results have also been investigated. Numerical studies including simulated experiments and an application to AIDS data verify the validity of the proposed estimators.

Suggested Citation

  • Yang Sun & Xiangzhong Fang, 2024. "Robust estimators of functional single index models for longitudinal data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 53(19), pages 6869-6890, October.
    • Handle: RePEc:taf:lstaxx:v:53:y:2024:i:19:p:6869-6890
    DOI: 10.1080/03610926.2023.2253939
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