The MLE is minimax optimal for LGC
<|reference_start|>The MLE is minimax optimal for LGC: We revisit the recently introduced Local Glivenko-Cantelli setting, which studies distribution-dependent uniform convegence rates of the Maximum Likelihood Estimator (MLE). In this work, we investigate generalizations of this setting where arbitrary estimators are allowed rather than just the MLE. Can a strictly larger class of measures be learned? Can better risk decay rates be obtained? We provide exhaustive answers to these questions -- which are both negative, provided the learner is barred from exploiting some infinite-dimensional pathologies. On the other hand, allowing such exploits does lead to a strictly larger class of learnable measures.<|reference_end|>
@article{cohen2024the,
    title={The MLE is minimax optimal for LGC},
    author={Doron Cohen, Aryeh Kontorovich, Roi Weiss},
    journal={arXiv preprint arXiv:2410.02835},
    year={2024},
    archivePrefix={arXiv},
    eprint={2410.02835},
    primaryClass={math.ST cs.LG stat.ME stat.TH}
}