## A Joint Central Limit Theorem for the Sample Mean and Regenerative Variance Estimator
*P. W. Glynn and D. L. Iglehart*
* Annals of Operations Research*, Vol. 8, 41-55 (1987)
Let {V(k): k ≥ 1} be a sequence of independent, identically distributed
random vectors in R^{d} with mean vector μ. The mapping g is a twice differentiable
mapping from R^{d} to R^{1}. Set r = g(μ). A bivariate central limit theorem is proved
involving a point estimator for r and the asymptotic variance of this point estimate.
This result can be applied immediately to the ratio estimation problem that arises
in regenerative simulation. Numerical examples show that the variance of the
regenerative variance estimator is not necessarily minimized by using the "return
state" with the smallest expected cycle length. |