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

10 papers

stat.CO2025

Quasi-Monte Carlo with one categorical variable

Valerie N. P. Ho, Art B. Owen, Zexin Pan

We study randomized quasi-Monte Carlo (RQMC) estimation of a multivariate integral where one of the variables takes only a finite number of values. This problem arises when the var…

math.NA2024

Skewness of a randomized quasi-Monte Carlo estimate

Zexin Pan, Art B. Owen

Some recent work on confidence intervals for randomized quasi-Monte Carlo (RQMC) sampling found a surprising result: ordinary Student $t$ 95% confidence intervals based on a modest…

math.NA2023

Computable error bounds for quasi-Monte Carlo using points with non-negative local discrepancy

Michael Gnewuch, Peter Kritzer, Art B. Owen +1

Let $f : [0, 1]^{d} \to R$ be a completely monotone integrand as defined by Aistleitner and Dick (2015) and let points $x_{0}, \dots, x_{n - 1} \in [0, 1]^{d}$ hav…

math.NA2023

Gain coefficients for scrambled Halton points

Art B. Owen, Zexin Pan

Randomized quasi-Monte Carlo, via certain scramblings of digital nets, produces unbiased estimates of $\int_{[0, 1]^{d}} f (x) d x$ with a variance th…

math.NA2022★ 2 cited

Super-polynomial accuracy of multidimensional randomized nets using the median-of-means

Zexin Pan, Art B. Owen

We study approximate integration of a function $f$ over $[0, 1]^{s}$ based on taking the median of $2 r - 1$ integral estimates derived from independently randomized $(t, m, s)$ -nets in ba…

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…

math.ST2018

$L_{p}$ and almost sure convergence of estimation on heavy tail index under random censoring

Yunyi Zhang, Jiazheng Liu, Zexin Pan +1

In this paper, we prove $L_{p}, p \geq 2$ and almost sure convergence of tail index estimator mentioned in \cite{grama2008} under random censoring and several assumptions. $p$ th mome…

math.ST2018

Monotone function estimator and its application

Yunyi Zhang, Dimitris N. Politis, Jiazheng Liu +1

In this paper, the model $Y_{i} = g (Z_{i}), i = 1, 2, ..., n$ with $Z_{i}$ being random variables with known distribution and $g (x)$ being unknown strictly increasing function is proposed and…

Quasi-Monte Carlo with one categorical variable

Skewness of a randomized quasi-Monte Carlo estimate

Computable error bounds for quasi-Monte Carlo using points with non-negative local discrepancy

Gain coefficients for scrambled Halton points

Super-polynomial accuracy of multidimensional randomized nets using the median-of-means

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

Where are the logs?

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

Lp​ and almost sure convergence of estimation on heavy tail index under random censoring

Monotone function estimator and its application

$L_{p}$ and almost sure convergence of estimation on heavy tail index under random censoring