Extensible grid sampling for quantile estimation with confidence intervals

主講人：何志堅 華南理工大學(xué)教授

時間：2023年7月12日9：30

地點：三號樓332室

舉辦單位：數(shù)理學(xué)院

主講人介紹：何志堅，華南理工大學(xué)數(shù)學(xué)學(xué)院教授、博導(dǎo)、副院長。2015年于清華大學(xué)獲得理學(xué)博士學(xué)位。研究興趣為隨機計算方法與不確定性量化，特別是擬蒙特卡羅方法的理論和應(yīng)用研究。相關(guān)研究成果發(fā)表在統(tǒng)計學(xué)四大期刊Journal of the Royal Statistical Society: Series B，計算科學(xué)重要期刊SIAM Journal on Numerical Analysis，SIAM Journal on Scientific Computing，Mathematics of Computation，和運籌管理權(quán)威期刊European Journal of Operational Research等。博士論文獲得新世界數(shù)學(xué)獎銀獎。主持兩項國家自然科學(xué)基金項目以及兩項省部級項目。

內(nèi)容介紹：Hilbert space-filling curve (HSFC) is continuous mapping from to for any . HSFC-based numerical integration of d-dimensional functions uses only one-dimensional (extensible) stratification inputs. It improves the error rate of Monte Carlo sampling while retaining asymptotic normality. This work studies HSFC sampling for quantile estimation. We show that under certain conditions, the HSFC-based quantile estimator is asymptotically normal and the asymptotic variance is of . We then develop an asymptotic confidence interval for quantiles that are estimated via simulation using HSFC. This is joint work with Jingyu Tan and Xiaoqun Wang.