Minimax Estimation

Minimax estimation asks how accurately an unknown quantity can be recovered in the hardest case within a specified model, and how many observations are needed. Researchers establish upper bounds for concrete estimators and lower bounds that apply to every method, often using regularization, aggregation, thresholding, and information-theoretic tools such as Fano's and Le Cam's methods. The framework covers settings including nonparametric regression, sparse covariance and distribution estimation, one-bit data, dependent observations, and differential privacy. A central challenge is understanding when adaptation to unknown structure is possible without extra cost, especially when privacy, contamination, or computational limits change the achievable rates.