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Robust parameter estimation of regression models under weakened moment assumptions

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  • Li, Kangqiang
  • Tang, Songqiao
  • Zhang, Lixin

Abstract

This paper provides some extended results on estimating parameter matrix of several regression models when the covariate or response possesses weaker moment condition. We study the M-estimator of Fan et al. (2021) for matrix completion model with (1+ϵ)-th moment noise. The corresponding phase transition phenomenon is observed. When 1>ϵ>0, the robust estimator possesses a slower convergence rate compared with previous literature. For high dimensional multiple index coefficient model, we propose an improved estimator via applying the element-wise truncation method to handle heavy-tailed data with finite fourth moment. The extensive simulation study validates our theoretical results.

Suggested Citation

  • Li, Kangqiang & Tang, Songqiao & Zhang, Lixin, 2022. "Robust parameter estimation of regression models under weakened moment assumptions," Statistics & Probability Letters, Elsevier, vol. 191(C).
    • Handle: RePEc:eee:stapro:v:191:y:2022:i:c:s0167715222001912
    DOI: 10.1016/j.spl.2022.109678
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    References listed on IDEAS

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    1. Jianqing Fan & Quefeng Li & Yuyan Wang, 2017. "Estimation of high dimensional mean regression in the absence of symmetry and light tail assumptions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 247-265, January.
    2. Shujie Ma & Peter X.-K. Song, 2015. "Varying Index Coefficient Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 341-356, March.
    3. Marco Avella-Medina & Heather S Battey & Jianqing Fan & Quefeng Li, 2018. "Robust estimation of high-dimensional covariance and precision matrices," Biometrika, Biometrika Trust, vol. 105(2), pages 271-284.
    4. Qiang Sun & Wen-Xin Zhou & Jianqing Fan, 2020. "Adaptive Huber Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 254-265, January.
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