Sub-Gaussian Concentration and Entropic Normality of the Maximum Likelihood Estimator

arXiv:2605.07107 · cs.IT, math.IT, math.ST, stat.ML, stat.TH · Submitted 2026-05-08 · Read on arXiv

cs.IT, math.IT, math.ST, stat.ML, stat.TH

Submitted: 2026-05-08

Updated: 2026-08-30

Terminology

• Fisher Information — 10× in this paper · explained in 3 episodes
• Consistency — 9× in this paper · explained in 3 episodes
• Score Function — 6× in this paper · explained in 4 episodes
• Core — 1× in this paper · explained in 2 episodes
• Wasserstein Distance — 1× in this paper · explained in 4 episodes

Sources

• On Learning-Curve Monotonicity for Maximum Likelihood Estimators
• Asymptotics of the maximum likelihood estimator of the location parameter of Pearson Type VII distribution
• Monotonicity of Entropy and Fisher Information: A Quick Proof via Maximal Correlation

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