Events

MAD Seminar : On the tight statistical analysis of a maximum likelihood estimator based on profiles

Speaker: Yanjun Han

Location: 60 Fifth Avenue, Room Auditorium Hall 150, Center for Data Sci

Date: Thursday, November 4, 2021

This talk, will provide a tight statistical analysis of the PMLE under the discrete distribution model. First, an analogy is established between the MLE and PMLE: the MLE is a minimax rate-optimal estimator of the unknown distribution, while the PMLE is a minimax rate-optimal estimator of the unknown distribution modulo permutation. Second, for estimating symmetric functionals of distributions, we show that plugging the same PMLE into different functionals universally attains their optimal sample complexities, provided that the target accuracy level exceeds a given threshold. Below this tight threshold, any adaptive approach (including the PMLE) fails to be universally optimal, and an exact penalty for adaptation is characterized. Finally, we generalize our analysis for discrete distribution models to Gaussian sequence models and others.