Revision as of 20:29, 14 March 2013 (edit) Addbot (talk \| contribs) m (Bot: Migrating 1 interwiki links, now provided by Wikidata on d:q3554721) ← Previous edit		Revision as of 09:34, 5 May 2014 (edit) (undo) Yobot (talk \| contribs) m (WP:CHECKWIKI error fixes using AWB (10093)) Next edit →
The '''control variates''' method is a [[variance reduction]] technique used in [[Monte Carlo methods]]. It exploits information about the errors in estimates of known quantities to reduce the error of an estimate of an unknown quantity.<ref>Glasserman, P. (2004). ''Monte Carlo Methods in Financial Engineering''. New York: Springer. ISBN 0-387-00451-3 (p. 185)</ref> ==Underlying principle== Let the unknown [[Parameter#~~Statistics_and_econometrics~~Statistics and econometrics\|parameter]] of interest be <math>\mu</math>, and assume we have a [[statistic]] <math>m</math> such that the [[expected value]] of ''m'' is μ: <math>\mathbb{E}\left[m\right]=\mu</math>, i.e. ''m'' is an [[bias of an estimator\|unbiased estimator]] for μ. Suppose we calculate another statistic <math>t</math> such that <math>\mathbb{E}\left[t\right]=\tau</math> is a known value. Then :<math>m^\star = m + c\left(t-\tau\right) \, </math> :<math>c^\star = - \frac{\textrm{Cov}\left(m,t\right)}{\textrm{Var}\left(t\right)}; </math> minimizes the variance of <math>m^{\star}</math>, and that with this choice, :<math>\begin{align} {{refimprove\|date=August 2011}} ==Notes== <references/> ==References== * Ross, Sheldon M. (2002) ''Simulation'' 3rd edition ISBN 978-0-12-598053-1

Control variates: Difference between revisions

Control variates (edit)

Revision as of 09:34, 5 May 2014