Density Estimation by Randomized Quasi-Monte Carlo

We consider the problem of estimating density a random variable $X$ that can be sampled exactly by Monte Carlo (MC). investigate effectiveness replacing MC randomized quasi (RQMC) or stratified sampling over unit cube, to reduce integrated variance (IV) and mean square error (MISE) for kernel estimators. show theoretically empirically RQMC estimators achieve substantial reductions IV MISE, even faster convergence rates than in some situations, while leaving bias unchanged. also bounds obtained via traditional Koksma-Hlawka-type inequality are much too loose useful when dimension exceeds few units. describe an alternative way estimate IV, good bandwidth, under stratification, we MISE reduced significantly high-dimensional settings.