Cramér–von Mises variance estimators for simulations

Cramér–von Mises variance estimators for simulations

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Article ID: iaor20011070
Country: United States
Volume: 47
Issue: 2
Start Page Number: 299
End Page Number: 309
Publication Date: Mar 1999
Journal: Operations Research
Authors: , ,
Keywords: statistics: inference
Abstract:

We study estimators for the variance parameter σ  2 of a stationary process. The estimators are based on weighted Cramér–von Mises statistics and certain weightings yield estimators that are ‘first-order unbiased’ for σ  2. We derive an expression for the asymptotic variance of the new estimators; this expression is then used to obtain the first-order unbiased estimator having the smallest variance among fixed-degree polynomial weighting functions. Our work is based on asymptotic theory; however, we present exact and empirical examples to demonstrate the new estimators’ small-sample robustness. We use a single batch of observations to derive the estimators’ asymptotic properties, and then we compare the new estimators among one another. In real-life applications, one would use more than one batch; we indicate how this generalization can be carried out.

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