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This paper establishes monotonicity guarantees for maximum likelihood estimators (MLE) in various parametric settings, particularly focusing on Gaussian and Gamma distributions. It demonstrates that the average performance of MLE improves with more data, confirming complete monotonicity for forward KL divergence in these models. The results were derived with the assistance of the GPT-5.2 Pro model, which generated proofs and extended findings without human intervention in the initial stages.

Author

creatiffcreation

Language

EN