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

Abstract

Standard dose response models, namely, the multistage Weibull, logistic and log-logistic models are considered. These models involve two parameters ${\mathit{\theta }}_0$ and ${\mathit{\theta }}_1$ , and we assume ${\mathit{\theta }}_0$ to be known. The maximum likelihood and Berkson’s minimum chi-square methods are employed to estimate the parameter ${\mathit{\theta }}_1$ in each model. The mean squared errors of the maximum likelihood and Berkson’s minimum chi-square estimators ${\hat{\mathit{\theta }}}_1$ are derived asymptotically to the order of approximation ${\mathit{n}}^{-2}$ . 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.