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.
This application is a continuation-in-part of U.S. patent application Ser. No. 10/983,346, filed on Nov. 8, 2004. This application is also a continuation-in-part of copending U.S. patent application Ser. No. 10/056,682 and U.S. patent application Ser. No. 10/056,683, now U.S. Pat. No. 7,080,136, filed concurrently on Jan. 24, 2002, and both of which claim priority to U.S. Provisional Application Ser. No. 60/277,123 ("Control Of Volume And Variance In Network Management"), filed Mar. 18, 2001 and U.S. Provisional Application Ser. No. 60/300,587 ("Charging from Sampled Network Usage"), filed Jun. 22, 2001. The 10/983,346 application also claims the benefit of U.S. Provisional Application No. 60/518,198 filed on Nov. 7, 2003. This application also claims priority to U.S. Provisional Application Ser. No. 60/700,585 filed on Jul. 19, 2005. Each of the aforementioned applications is incorporated herein by reference.
