On an asymptotic comparison of the maximum likelihood and Berkson's minimum chi-square estimators in some standard dose response models with one unknown parameter

Standard dose response models, namely, the multistage Weibull, logistic and log-logistic models are considered. These models involve two parameters θ 0 and θ 1 , and we assume θ 0 to be known. The maximum likelihood and Berkson’s minimum chi-square methods are employed to estimate the parameter θ 1 in each model. The mean squared errors of the maximum likelihood and Berkson’s minimum chi-square estimators θ ˆ 1 are derived asymptotically to the order of approximation n − 2 . The results show that the mean squared errors of the maximum likelihood and Berkson’s minimum chi-square estimators behave differently for different dose groups and dose levels.