Z. Pan

activity

20182025

most citedThe nonzero gain coefficients of Sobol's sequences are always powers of two

4 citations · 8 across the 9 of their papers we have counts for

collaborators

Showing 2021Show all

3 papers · 1 filter

stat.CO2021★ 2 cited

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 $∣ f^{(k)} (1/2) ∣ \leq A α^{k} k!$ for some constant $A$ and $α < 2$ . We show that the median estimate of $μ = \int_{0}^{1} f (x) d x$ under random line…

math.NA2021

Where are the logs?

Art B. Owen, Zexin Pan

The commonly quoted error rates for QMC integration with an infinite low discrepancy sequence is $O (n^{- 1} lo g (n)^{r})$ with $r = d$ for extensible sequences and $r = d - 1$ otherwise. Suc…

math.NA2021★ 4 cited

The nonzero gain coefficients of Sobol's sequences are always powers of two

Zexin Pan, Art B. Owen

When a plain Monte Carlo estimate on $n$ samples has variance $σ^{2} / n$ , then scrambled digital nets attain a variance that is $o (1/ n)$ as $n \to \infty$ . For finite $n$ and an adversa…