In this work, we develop an approach mentioned by da Veiga and Gamboa in 2013. It consists in extending the very interestingpoint of view introduced in \cite{gine2008simple} to estimate general nonlinear integral functionals of a density on the real line, by using empirically a kernel estimator erasing the diagonal terms. Relaxing the positiveness assumption on the kernel and choosing a kernel of order large enough, we are able to prove a central limit theorem for estimating Sobol' indices of any order (the bias is killed thanks to this signed kernel).

翻译：本研究发展了一种由da Veiga和Gamboa于2013年提出的方法。该方法扩展了\cite{gine2008simple}中引入的极其有趣的观点，通过经验性地使用消除对角项的非参数核估计器，来估计实直线上密度的一般非线性积分泛函。通过放宽核的正性假设并选择足够高阶的核，我们能够证明估计任意阶Sobol'指数的中心极限定理（得益于该符号核，偏差被消除）。