Optimal combination of sampled measurements

摘要

Two regularized estimators that avoid the pathologies associated with variance estimation are disclosed. The regularized variance estimator adds a contribution to estimated variance representing the likely error, and hence ameliorates the pathologies of estimating small variances while at the same time allowing more reliable estimates to be balanced in the convex combination estimator. The bounded variance estimator employs an upper bound to the variance which avoids estimation pathologies when sampling probabilities are very small.