A Sequential Fixed-Size Confidence Interval Estimation for Positive Parameters with Applications in Statistical Ecology

• Activity Number: 645
• Type: Contributed
• Date/Time: Thursday, August 8, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics and the Environment
• Author(s): Swarnali Banerjee*+ and Nitis Mukhopadhyay
• Companies: University of Connecticut and University of Connecticut
• Keywords: ecology ; entomology ; infestation ; sequential ; Negative Binomial ; confidence interval

Abstract

We focus on count data from statistical ecology. Anscombe (1949, Biometrics) emphasized negative binomial (NB) modeling for overdispersed count data. He proposed a NB distribution with two parameters - mean (>0) and clumping or thatching parameter k (finite). Many existing methodologies, both non-sequential and sequential, were reviewed by Mukhopadhyay and Banerjee (2012, under submission). Willson and Folks (1983) developed a sequential fixed-size confidence interval methodology for NB mean with k known, but it had an undesirable property that the lower confidence limit might not be positive. Hence we (joint work with Professor Mukhopadhyay) have introduced an appropriate alternative sequential fixed-size confidence interval for NB mean with both upper (and lower) confidence limit(s) positive assuming k known. The procedure enjoys asymptotic consistency and first-order asymptotic efficiency and its applications in ecology are widespread and useful. The new methodology is compared with that of Willson and Folks followed by a real data application from insect infestation with very encouraging results. Time permitting, some extensions may be included.