Corpus ID: 221340917

Out-of-sample error estimate for robust M-estimators with convex penalty

@article{Bellec2020OutofsampleEE,
  title={Out-of-sample error estimate for robust M-estimators with convex penalty},
  author={Pierre C. Bellec},
  journal={arXiv: Statistics Theory},
  year={2020}
}
A generic out-of-sample error estimate is proposed for robust $M$-estimators regularized with a convex penalty in high-dimensional linear regression where $(X,y)$ is observed and $p,n$ are of the same order. If $\psi$ is the derivative of the robust data-fitting loss $\rho$, the estimate depends on the observed data only through the quantities $\hat\psi = \psi(y-X\hat\beta)$, $X^\top \hat\psi$ and the derivatives $(\partial/\partial y) \hat\psi$ and $(\partial/\partial y) X\hat\beta$ for fixed… Expand

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