A Finite Sample Study of a New Adaptive Nonparametric Method for Quantal Bioassay in Diverse Models

• Activity Number: 518
• Type: Contributed
• Date/Time: Wednesday, August 4, 2010 : 10:30 AM to 12:20 PM
• Sponsor: ENAR
• Author(s): Lizhen Lin*+ and Rabi Bhattacharya
• Companies: The University of Arizona and The University of Arizona
• Keywords: dose-response curve ; effective dosage ; benchmark analysis ; non-parametric curve estimation ; integrated mean squared error ; asymptotic normality

Abstract

We present the finite sample performance of a new nonparametric method for benchmark analysis and bioassay in more diverse models than the ones that have been studied in Bhattacharya and Lin (2010b). The new method, termed NAM, improves upon the PAV-based procedure due to Bhattacharya and Kong (2007). The asymptotic theory for the new estimates is derived in Bhattacharya and Lin (2010a) and shows that the MISEs (mean integrated squared errors) of the estimate of the dose-response curve F and the estimate of the effective dosage curve F^{-1} achieve the optimal rate O(N^{-4/5}). The asymptotic distribution of the estimate of the quantile curve F^{-1} is also derived. The comparison is carried out among the new method and other nonparametric methods including the leading kernel-based method, termed DNP, due to Dette et al.(2005) and Dette and Scheder (2010).