Theory of Adaptive Estimation

Explore the modern theory of adaptive estimation in this 45-minute talk by Oleg Lepski. Delve into a universal estimation procedure based on random selection from estimator collections, adhering to general assumptions. Examine an upper bound for the proposed estimator's risk within an abstract statistical model, utilizing operator commutativity and upper functions for positive random functionals. Discover how this single oracle inequality can be applied to various problems across different statistical models. Follow the presentation's outline, covering statistical experiments, estimation targets, minimax approaches, and adaptive estimation techniques. Investigate specific examples, including density models and white Gaussian noise models, to better understand the practical applications of these concepts.

Intro
Outline of the talk.
Statistical experiment and estimation target.
Statistical experiment. C-risk.
Examples of statistical experiments. Density mod
Examples of statistical experiments. WGN model
Examples of estimation targets.
Minimax approach.
Minimax adaptive approach. Criterion of optimali
Minimax adaptive approach. Fundamental proble
Minimax adaptive approach. Example.
Minimax adaptive approach. Estimation of || | || 2.
Problem formulation.
Selection rule. Notations and assumptions.
E-selection rule for estimating G.
Relation to the adaptive estimation.
Examples of estimator's families satisfying Apert