Inference Concerning the Negative Binomial Dispersion Parameter, with Applications to Tumor Data

• Activity Number: 73
• Type: Contributed
• Date/Time: Sunday, August 2, 2009 : 4:00 PM to 5:50 PM
• Sponsor: Section on Risk Analysis
• Author(s): Krishna K. Saha*+ and Sudhir R. Paul
• Companies: Central Connecticut State University and University of Windsor
• Keywords: Bootstrap confidence interval ; coverage probability ; dispersed parameter ; maximum likelihood ; negative binomial model ; tumor data

Abstract

Inference concerning the negative binomial dispersion parameter is important in many biological investigations. Properties of its maximum likelihood estimator and its bias corrected version have been studied extensively, mainly in terms of bias and efficiency. However, little has been done with constructing confidence intervals for the negative binomial dispersion parameter. This paper studies the behavior of six such procedures based on the following: the method of moments estimate (MME), the maximum likelihood estimate (MLE), the bias-corrected MLE (BCMLE), and their respective bootstrap versions. Simulation results indicate, in general, severe under-coverage for the three methods based on the MME, MLE and BCMLE, but their bootstrap versions improve this problem significantly. An example with applications to tumor data is presented.