A test-based regression estimator achieves a nonasymptotic oracle inequality for the ℓ1 loss under possibly heavy-tailed and heteroscedastic errors, and provably beats the least squares estimator when a few error variances are huge.
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Estimating a regression function under possible heteroscedastic and heavy-tailed errors. Application to shape-restricted regression
A test-based regression estimator achieves a nonasymptotic oracle inequality for the ℓ1 loss under possibly heavy-tailed and heteroscedastic errors, and provably beats the least squares estimator when a few error variances are huge.