Simulation Testing of Unbiasedness of Variance Estimators

Abstract

In this article I address the evaluation of estimators of variance for parameter estimates. Given an unbiased estimator X of a parameter θ, and an estimator V of the variance of X, how does one test (via simulation) whether V is an unbiased estimator of the variance of X? The derivation of the test statistic illustrates the need for care in substituting consistent estimators for unknown parameters.

Key Words:

• Monte Carlo method
• U statistics