Density Estimation by Randomized Quasi-Monte Carlo
Density Estimation by Randomized Quasi-Monte Carlo
复制标题
通过随机准蒙特卡罗进行密度估计
DOI：
10.1137/19m1259213
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Puchhammer, Florian
中科院分区：
文献类型：
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作者：
Ben Abdellah, Amal;L'Ecuyer, Pierre;Owen, Art B.;Puchhammer, Florian
本文考虑了用蒙特卡罗方法估计可精确抽样的随机变量的密度的问题。我们调查的有效性，取代MC随机准MC（RQMC）或分层抽样的单位立方体，以减少集成方差（IV）和平均集成平方误差（MISE）的核密度估计。我们从理论上和经验表明，RQMC和分层估计可以实现大幅减少的IV和MISE，甚至更快的收敛速度比MC在某些情况下，同时保持偏差不变。我们还表明，通过传统的Koksma-Hlawka型不等式RQMC的方差界是太松散的，是有用的，当问题的维数超过几个单位。我们描述了另一种方法来估计IV，一个良好的带宽，和MISE，根据RQMC或分层，我们的经验表明，在某些情况下，MISE可以显着减少，即使在高维设置。
We consider the problem of estimating the density of a random variablethat can be sampled exactly by Monte Carlo (MC). We investigate the effectiveness of replacing MC by randomized quasi-MC (RQMC) or by stratified sampling over the unit cube to reduce the integrated variance (IV) and the mean integrated square error (MISE) for kernel density estimators. We show theoretically and empirically that the RQMC and stratified estimators can achieve substantial reductions of the IV and the MISE, and even faster convergence rates than MC in some situations, while leaving the bias unchanged. We also show that the variance bounds obtained via a traditional Koksma--Hlawka-type inequality for RQMC are much too loose to be useful when the dimension of the problem exceeds a few units. We describe an alternative way to estimate the IV, a good bandwidth, and the MISE, under RQMC or stratification, and we show empirically that in some situations, the MISE can be reduced significantly even in high-dimensional settings.
R 中的随机 Halton 算法
DOI：
--
发表时间：
2017
期刊：
arXiv.org
影响因子：
--
作者：
A. Owen
通讯作者：
A. Owen