Comparison of bias-reducing methods for estimating the parameter in dilution series

Abstract

Ten different estimators of the parameter in a limiting or serial dilution assay are compared. Eight of them are constructed to reduce the bias of the commonly used maximum likelihood estimator. Extensive Monte Carlo experiments using various designs, and practical considerations, suggest that a particular jackknife version of the maximum likelihood estimator is preferred, provided that the design is not too small.

Keywords:

• limiting and serial dilution assays
• maximum likelihood
• jackknife methods
• bootstrap methods
• min-imum cht-square
• Monte Carlo experiments
• experimental design