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math.ST2023
Error estimation and adaptive tuning for unregularized robust M-estimator
Pierre C. Bellec, Takuya Koriyama
We consider unregularized robust M-estimators for linear models under Gaussian design and heavy-tailed noise, in the proportional asymptotics regime where the sample size n and the…
math.ST2023
Existence of solutions to the nonlinear equations characterizing the precise error of M-estimators
Pierre C. Bellec, Takuya Koriyama
Major progress has been made in the previous decade to characterize the asymptotic behavior of regularized M-estimators in high-dimensional regression problems in the proportional…
math.ST2023
Corrected generalized cross-validation for finite ensembles of penalized estimators
Pierre C. Bellec, Jin-Hong Du, Takuya Koriyama +2
Generalized cross-validation (GCV) is a widely-used method for estimating the squared out-of-sample prediction risk that employs a scalar degrees of freedom adjustment (in a multip…