  Estimating the density of a continuous random variable X has been studied
extensively in statistics, in the setting where n independent observations of X
are given a priori and one wishes to estimate the density from that. Popular
methods include histograms and kernel density estimators. In this review paper,
we are interested instead in the situation where the observations are generated
by Monte Carlo simulation from a model. Then, one can take advantage of
variance reduction methods such as stratification, conditional Monte Carlo, and
randomized quasi-Monte Carlo (RQMC), and obtain a more accurate density
estimator than with standard Monte Carlo for a given computing budget. We
discuss several ways of doing this, proposed in recent papers, with a focus on
methods that exploit RQMC. A first idea is to directly combine RQMC with a
standard kernel density estimator. Another one is to adapt a simulation-based
derivative estimation method such as smoothed perturbation analysis or the
likelihood ratio method to obtain a continuous estimator of the cdf, whose
derivative is an unbiased estimator of the density. This can then be combined
with RQMC. We summarize recent theoretical results with these approaches and
give numerical illustrations of how they improve the convergence of the mean
square integrated error.
