Parametric and nonparametric estimators of ED100α

In bioassay, the logit model is the most widely used parametric model. However, the exact form of the response curve is usually unknown and even very complicated, so it is likely that the true model does not follow the logit model. Therefore, according to well-known asymptotic results, when the sample size is very large, we should probably use the non-parametric regression rather than the logit model unless the exact form of the true response curve is known. In practice, however, we can not increase the sample size infinitely, so the asymptotic result would not be so useful. In this article, we would like to compare the small sample properties of the logit model and the non-parametric estimator. As the non-parametric method, we choose the locally weighted quasi-likelihood estimator. A Monte Carlo study was done under various circumstances, and it turned out that the locally weighted quasi-likelihood estimator is very competitive in the small sample situation.