Estimating Positive Parameters Using Fixed-Accuracy Confidence Interval Methods with Applications in Health and Environment

• Activity Number: 146
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics in Defense and National Security
• Author(s): Swarnali Banerjee* and Nitis Mukhopadhyay
• Companies: Old Dominion University and University of Connecticut
• Keywords: Confidence Interval ; Environmental Statistics ; First-order properties ; Fixed-Accuracy ; ML estimator ; Sequential Methods

Abstract

We propose a general procedure of estimating any positive parameter using such sequential fixed-accuracy confidence intervals. Estimation of positive parameters is essential in the areas of ecology, biology, medicine, nuclear power, study of cell membranes and others. For this methodology we have considered a consistent estimator of the parameter - it's maximum likelihood estimator. Beyond ecology, the procedure finds its applications in other affected by some disease, number of cells under genetic mutation, etc. Mukhopadhyay and Banerjee (2014b) developed a fixed-accuracy sequential confidence interval methodology for the mean of a negative binomial (NB) distribution with its thatch parameter unknown with applications in statistical ecology. In this paper, we develop a general structure for fixed-accuracy sequential confidence interval estimation methodology for any positive parameter of an arbitrary distribution which may be discrete or continuous. We construct our confidence interval, [T /d, dT] with d > 1, using a maximum likelihood (ML) estimator T. The methodology satisfies attractive properties such as asymptotic (as d ? 1+) consistency and asymptotic first-order efficiency