Minimal-MSE linear combinations of variance estimators of the sample mean

ABSTRACT

We continue our investigation of linear combinations of variance-of-the-sample-mean estimators that are parameterized by batch size. First we state the mse-optimal linear-combination weights in terms of the bias vector and the covariance matrix of the component estimators for two cases: weights unconstrained and weights constrained to sum to one. Then we report a small numerical study that demonstrates mse reduction of about 80% for unconstrained weights and about 30% for constrained weights. The mse's and the percent reductions are similar for all four estimator types considered. Such large mse reductions could not be achieved in practice, since they assume knowledge of unknown parameters, which would have to be estimated. Optimal-weight estimation is not considered here.

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing

Additional Classification:
  I. Computing Methodologies
  I.6 SIMULATION AND MODELING

General Terms:
Design, Measurement, Performance, Theory, Verification