Robust parameter estimation of regression models under weakened moment assumptions

Kangqiang Li, Songqiao Tang and Lixin Zhang

Statistics & Probability Letters, 2022, vol. 191, issue C

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.

Keywords: Linear and nonlinear statistical models; Heavy-tailed data; Element-wise truncation; Robust estimation (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spl.2022.109678

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