Adaptive estimation of nonparametric functionals

Lin Liu, Rajarshi Mukherjee, James Robins, Eric Tchetgen Tchetgen

Abstract: 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 para- metric and nonparametric regimes of estimation and are automatically adaptive and semiparametric efficient in the regime of parametric convergence rate.