On Minimum Distance Estimation in Dose Response Studies

Abstract

In this thesis, two robust and efficient methods of estimation are examined in dose-response studies context. In particular, we investigate the minimum Hellinger distance estimation and symmetric chi-squared distance methods of estimation. We support our theoretical results with extensive finite sample simulation studies. Based on the minimum Hellinger distance and symmetric chi-squared distance approaches, new estimators of the regression parameters are derived for logistic and probit models. Then their asymptotic properties such as consistency and asymptotic normality are investigated. It is shown that our minimum Hellinger distance estimator is asymptotically equivalent to the traditional estimators derived using the maximum likelihood and weighted least squares approaches. Simulation studies are used to demonstrate that the new estimators work as good as the traditional estimators and most often outperforms them when a contamination occurs in the data. Lastly, the proposed methods are used to estimate the critical dose.