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Robust shrinkage estimation and selection for functional multiple linear model through LAD loss

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  • Huang, Lele
  • Zhao, Junlong
  • Wang, Huiwen
  • Wang, Siyang

Abstract

In functional data analysis (FDA), variable selection in regression model is an important issue when there are multiple functional predictors. Most of the existing methods are based on least square loss and consequently sensitive to outliers in error. Robust variable selection procedure is desirable. When functional predictors are considered, both non-data-driven basis (e.g. B-spline) and data-driven basis (e.g. functional principal component (FPC)) are commonly used. The data-driven basis is flexible and adaptive, but it raise some difficulties, since the basis must be estimated from data.

Suggested Citation

  • Huang, Lele & Zhao, Junlong & Wang, Huiwen & Wang, Siyang, 2016. "Robust shrinkage estimation and selection for functional multiple linear model through LAD loss," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 384-400.
    • Handle: RePEc:eee:csdana:v:103:y:2016:i:c:p:384-400
    DOI: 10.1016/j.csda.2016.05.017
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    Cited by:

    1. Huiwen Wang & Shan Lu & Jichang Zhao, 2018. "Aggregating multiple types of complex data in stock market prediction: A model-independent framework," Papers 1805.05617, arXiv.org.
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    3. Gongming Shi & Tianfa Xie & Zhongzhan Zhang, 2020. "Statistical inference for the functional quadratic quantile regression model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(8), pages 937-960, November.
    4. Sanying Feng & Menghan Zhang & Tiejun Tong, 2022. "Variable selection for functional linear models with strong heredity constraint," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(2), pages 321-339, April.

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