Control variate technique: A constructive approach

Abstract

The technique of control variates requires that the user identify a set of variates that are correlated with the estimation variable and whose means are known to the user. We relax the known mean requirement and instead assume the means are to be estimated. We argue that this strategy can be beneficial in parametric studies, analyze the properties of controlled estimators, and propose a class of generic and effective controls in a parametric estimation setting. We discuss the effectiveness of the estimators via analysis and simulation experiments.

Better simulation metamodeling: The why, what, and how of stochastic kriging

“…Differentiating Y with respect to x is the basis for the infinitesimal perturbation analysis (IPA) method of estimating derivatives of y (Fu 2008). Borogovac and Vakili (2008) show that when ρ(x, x ) is large for x near x, it is possible to achieve large variance reduction in estimating the value of the response surface y at many nearby points; they also consider using derivatives of Y in their method. If a simulation at x provides estimates of the response y(x) and of its derivatives, this can improve metamodeling (Morris, Mitchell, and Ylvisaker 1993).…”

Monte Carlo Computation in Finance

“…The idea of database Monte Carlo (DBMC) is to invest computational effort in constructing a database which enables efficient estimation for a range of similar problems [16]. In finance, it is often important to solve a whole set of similar problems ( §3).…”

“…It may be possible to estimate µ(θ ) well with f (·, θ ) evaluated at only a small number n of points. DBMC has been implemented with stratification and control variates [16,96,97,98]. All but one of the methods in these papers are structured database Monte Carlo (SDMC) methods, in which further effort is expended in structuring the database: the database is sorted so that f (ω i ; θ 0 ) is monotone in i [98].…”

“…DBMC applied to control variates [16] leads to the idea of a quasi-control variate [31], i.e., a random variable used as a control variate even though its mean is unknown and merely estimated by Monte Carlo [85]. In DBMC, one can use f (u; θ 0 ) as a quasi-control variate, with estimated mean ∑ N i=1 f (ω i ; θ 0 )/N.…”

Control variates for sensitivity estimation

“…The user can follow the Estimated/Biased Control Variate approach (see (Schmeiser, Taaffe, and Wang 2001), (Pasupathy et al 2008), (Emsermann and Simon 2002)) where the means of the control variates are approximated or estimated via Monte Carlo. Alternatively, the DataBase Monte Carlo (DBMC) implementation proposed in (Borogovac andVakili 2008, Borogovac andVakili 2009) can be used, where, again, the means of the control variates need to be estimated via Monte Carlo. In either case, the implementation requires some computational setup cost.…”