Under finite moments and a local envelope growth condition, the least squares estimator in nonparametric regression can achieve minimax rates with heavy-tailed, covariate-dependent errors.
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On Least Squares Estimation under Heteroscedastic and Heavy-Tailed Errors
Under finite moments and a local envelope growth condition, the least squares estimator in nonparametric regression can achieve minimax rates with heavy-tailed, covariate-dependent errors.