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

Article type: Research Article

Authors: Srisodaphol, Wuttichai^a | Tiensuwan, Montip^{a; *} | Sinha, Bimal K^b

Affiliations: [a] Department of Mathematics, Faculty of Science, Mahidol University, Bangkok, Thailand | [b] Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, MD, USA

Correspondence: [*] Corresponding author: Montip Tiensuwan, Department of Mathematics, Faculty of Science, Mahidol University, Rama 6 Road, Bangkok 10400, Thailand. E-mail: [email protected].

Abstract: Standard dose response models, namely, the multistage Weibull, logistic and log-logistic models are considered. These models involve two parameters θ0 and θ1, and we assume θ0 to be known. The maximum likelihood and Berkson’s minimum chi-square methods are employed to estimate the parameter θ1 in each model. The mean squared errors of the maximum likelihood and Berkson’s minimum chi-square estimators θˆ1 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.

Keywords: Asymptotic comparison, Berkson's minimum chi-square, logistic model, log-logistic model, maximum likelihood, multistage Weibull model

DOI: 10.3233/MAS-2011-0161

Journal: Model Assisted Statistics and Applications, vol. 6, no. 1, pp. 21-38, 2011