Minimax Lower Bounds
Christophe Giraud · 2021
The goal of the statistician is to infer information as accurately as possible from data. From a theoretical perspective, when investigating a given statistical model. Deriving lower bounds is then a common task in mathematical statistics. This technique is then applied to show some optimality results on the model selection estimator. The minimax lower bound provides insightful information on the frontier between the statistical problems that can be successfully solved and those that are hopeless. Minimax risk is a popular notion in mathematical statistics in order to assess the optimality of an estimator. The typical objective of a theoretical statistician is to design an estimation procedure with a small computational complexity and which is minimax optimal. Has’minskii proposed to use Fano’s inequality for deriving lower bounds in non-parametric estimation problems.