Some New Perspectives on the Method of Control Variates

By Peter W. Glynn, Roberto Szechtman. 2002

105 citations recorded by the source corpus.

The method of control variates is one of the most widely used variance reduction techniques associated with Monte Carlo simulation. This paper studies the method of control variates from several different viewpoints, and establishes new connections between the method of control variates and: conditional Monte Carlo, antithetics, rotation sampling, stratification, and nonparametric maximum likelihood. We also develop limit theory for the method of control variates under weak assumptions on the estimator of the optimal control coefficient.

Subfields: Computational Theory and Mathematics, Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/09a97cd3bfd4c238fedfd625cb80e5b6ce2cecb3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Numerical Analysis

In Statistics and Probability

Citations in the corpus

Monte Carlo and Quasi-Monte Carlo Sampling (2009, methodology): “More connections between control variates and other variance reduction techniques are studied in [139].”
Control variates for quasi-Monte Carlo (2005, background): “However, combining VRTs often gives rise to complicated synergetic effects that are not always easy to analyze (see, e.g., Avramidis and Wilson, 1996; Glynn and Szechtman, 2002) and this applies to the RQMC–CV setup.”
A theory of statistical models for Monte Carlo integration (2003, background): “For good summaries, see Hammersley and Hanscomb (1964), Ripley (1987), Evans and Swartz (2000) or Liu (2001). For overviews on the computation of normalizing constants, see DiCiccio et al. (1997) or Gelman and Meng (1998).”
Monte Carlo with determinantal point processes (2016, methodology): “Another postprocessing technique with fast convergence relies on control variates [Glynn and Szechtman, 2002].”
On a Likelihood Approach for Monte Carlo Integration (2004, background): “Glynn and Szechtman (2000) also noted that the regression estimator is equivalent to the constrained MLE to first order, and gave a proof under the weaker condition that gj (x)/q1(x) has finite fourth moment under P1 for 1 ≤ j ≤ l.”
Control variates for estimation based on reversible Markov chain Monte Carlo samplers (2012, methodology): “…idea of using control variates, as in the case of simple Monte Carlo sampling with independent and identically distributed samples; see, for example, the standard texts of Robert and Casella (2004), Liu (2001) and Givens and Hoeting (2005) or Glynn and Szechtman (2002) for extensive discussions.”
Monte Carlo Gradient Estimation in Machine Learning (2019, background): “Gong and Ho (1987) introduced smoothed perturbation analysis as one variant of the pathwise derivative to address cases where the interchange of differentiation and integration is not applicable, such as when there are discontinuities in the cost function; and several other extensions of the estimat”