Super-polynomial accuracy of one dimensional randomized nets using the median-of-means

Zexin Pan, Art B. Owen

Let $f$ be analytic on $[0,1]$ with $|f^{(k)}(1/2)|\le A{\alpha }^{k}k!$ for some constant $A$ and $\alpha <2$. We show that the median estimate of $\mu ={\int }_0^{1}f(x)\mathrm{d}x$ under random line…