Likelihood-based methods for bias reduction in limiting dilution assays

Two likelihood-based methods for reducing the bias of the estimator of the parameter in a limiting dilution assay are compared with those using the jackknife. The maximum likelihood estimator, even after amendment so that its expectation exists, has positive bias which is removed by both likelihood-based methods and some versions of the jackknife. However, the variance of the resulting estimators is estimated reliably only for the likelihood-based methods; the estimate of the variance of the jackknife estimators can be in error by as much as 85%.