Generalized van Trees inequality: Local minimax bounds for non-smooth functionals and irregular statistical models

Understand

In a decision-theoretic framework, the minimax lower bound provides the worst-case performance of estimators relative to a given class of statistical models.

• For parametric and semiparametric models, the H\'{a}jek--Le Cam local asymptotic minimax (LAM) theorem provides the sharp local asymptotic lower bound.
• Despite its relative generality, this result comes with limitations as it only applies to the estimation of differentiable functionals under regular statistical models.
• On the other hand, minimax lower bound techniques such as Fano's or Assoud's are applicable in more general settings but are not sharp enough to imply the LAM theorem.