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.

翻译：我们根据无限维度模型的有限维度近似产生的二等U-统计学,为估算非参数功能提供了一般的适应性上限界限。然后,我们提供了理论产生与适应性上限和下限最佳匹配的功能的例子。我们的结果在参数性和非参数性估算系统中都是自动适应性的,在参数性趋同率制度中是自动适应性和半参数性的。