Cramer-von Mises variance estimators for simulations

We study estimators for the variance parameter sigma(2) of a stationary pro cess. The estimators are based on weighted Cramer-von Mises statistics, and certain weightings yield estimators that are "first-order unbiased" for si gma(2). We derive an expression for the asymptotic variance of the new esti mators; this expression is then used to obtain the first-order unbiased est imator having the smallest variance among fu;ed-degree polynomial weighting functions. Our work is based on asymptotic theory; however, we present exa ct and empirical examples to demonstrate the new estimators' small-sample r obustness. We use a single batch of observations to derive the estimators' asymptotic properties, and then we compare the new estimators among one ano ther. In real-life applications, one would use more than one batch; we indi cate how this generalization can be carried out.