Technical Note - Central Limit Theorems for Estimated Functions at Estimated PointsPeter W. Glynn, Lin Fan, Michael C. Fu, Jianqiang Hu, and Yijie Peng Operations Research, Volume 68, Issue 5 (2020). We provide a simple proof of the central limit theorem (CLT) for the estimator Y_n(X_n) as an estimate of E[Y(x^*)], where Y_n(·) is the sample mean estimator for the function E[Y(·)] and X_n is an estimator for x^*. Such estimators arise in a number of different simulation-based computational settings. We illustrate the methodology via applications to quantile estimation and related sensitivity analysis, as well as to computation of conditional value-at-risk. |