Control variates: Difference between revisions

m
(some links; expanded example a bit)
:<math>\rho_{m,t}=\textrm{Corr}\left(m,t\right); \, </math>
 
is the [[Pearson product-moment correlation coefficient|correlation coefficient]] of ''m'' and ''t''. The greater the value of <math>\vert\rho_{m,t}\vert</math>, the greater the [[variance reduction]] achieved.
 
In the case that <math>\textrm{Cov}\left(m,t\right)</math>, <math>\textrm{Var}\left(t\right)</math>, and/or <math>\rho_{m,t}\;</math> are unknown, they can be estimated across the Monte Carlo replicates. This is equivalent to solving a certain [[least squares]] system; therefore this technique is also known as '''regression sampling'''.