Robust parameter estimation of regression model with weaker moment
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This paper provides some extended results on estimating the parameter matrix of high-dimensional regression model when the covariate or response possess weaker moment condition. We investigate the M-estimator of Fan et al. (Ann Stat 49(3):1239–1266, 2021) for matrix completion model with (1+ϵ)-th moments. The corresponding phase transition phenomenon is observed. When ϵ≥ 1, the robust estimator possesses the same convergence rate as previous literature. While 1> ϵ>0, the rate will be slower. For high dimensional multiple index coefficient model, we also apply the element-wise truncation method to construct a robust estimator which handle missing and heavy-tailed data with finite fourth moment.
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