Adaptive Estimation of Nonparametric Functionals

Understand

We provide general adaptive upper bounds for estimating nonparametric functionals based on second order U-statistics arising from finite dimensional approximation of the infinite dimensional models.

• We then provide examples of functionals for which the theory produces rate optimally matching adaptive upper and lower bounds.
• Our results are automatically adaptive in both parametric and nonparametric regimes of estimation and are automatically adaptive and semiparametric efficient in the regime of parametric convergence rate.