Underlying Principle of The CRN Technique
Suppose and are the observations from the first and second configurations on the jth independent replication.
We want to estimate
If we perform n replications of each configuration and let
then and Z(n) = Σ Zj / n is an unbiased estimator of .
And since the 's are independent identically distributed random variables,
In case of independent sampling, i.e., no common random numbers used then Cov(X1j, X2j) = 0. But if we succeed to induce an element of positive correlation between X1 and X2 such that Cov(X1j, X2j) > 0, it can be seen from the equation above that the variance is reduced.
It can also be observed that if the CRN induces a negative correlation, i.e., Cov(X1j, X2j) < 0, this technique can actually backfire, where the variance is increased and not decreased (as intended).
Read more about this topic: Variance Reduction
Famous quotes containing the words underlying, principle and/or technique:
“The “female culture” has shifted more rapidly than the “male culture”; the image of the go-get ‘em woman has yet to be fully matched by the image of the let’s take-care-of-the-kids- together man. More important, over the last thirty years, men’s underlying feelings about taking responsibility at home have changed much less than women’s feelings have changed about forging some kind of identity at work.”
—Arlie Hochschild (20th century)
“We have been here over forty years, a longer period than the children of Israel wandered through the wilderness, coming to this Capitol pleading for this recognition of the principle that the Government derives its just powers from the consent of the governed. Mr. Chairman, we ask that you report our resolution favorably if you can but unfavorably if you must; that you report one way or the other, so that the Senate may have the chance to consider it.”
—Anna Howard Shaw (1847–1919)
“The audience is the most revered member of the theater. Without an audience there is no theater. Every technique learned by the actor, every curtain, every flat on the stage, every careful analysis by the director, every coordinated scene, is for the enjoyment of the audience. They are our guests, our evaluators, and the last spoke in the wheel which can then begin to roll. They make the performance meaningful.”
—Viola Spolin (b. 1911)