Density Estimation by Monte Carlo and Quasi-Monte Carlo
Abstract
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 cumulative density function (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.
Except where otherwise noted, this item's license is described as Reconocimiento-NoComercial-CompartirIgual 3.0 España
Ítems relacionados
Mostrando ítems relacionados por Título, autor o materia.
-
Ergodic transition in a simple model of the continuous double auction
Radivojevic, T.; Anselmi, J.; Scalas, E. (2014-12-31)We study a phenomenological model for the continuous double auction, whose aggregate order process is equivalent to two independent M/M/1 queues. The continuous double auction defines a continuous-time random walk for trade ... -
Modified Hamiltonian Monte Carlo for Bayesian Inference
Radivojevic, T.; Akhmatskaya, E. (2019-07-22)The Hamiltonian Monte Carlo (HMC) method has been recognized as a powerful sampling tool in computational statistics. We show that performance of HMC can be significantly improved by incorporating importance sampling and ... -
Monte Carlo and Quasi-Monte Carlo Density Estimation via Conditioning
L'Ecuyer, P.; Puchhammer, F.; Ben Abdellah, A. (2021)Estimating the unknown density from which a given independent sample originates is more difficult than estimating the mean, in the sense that for the best popular non-parametric density estimators, the mean integrated ...