STATISTICS COLLOQUIUM
Debanjan Bhattacharjee
Associate Professor
Department of Mathematics
Utah Valley University
Sequentially Estimating the Required Optimal Observed Number of Tagged Items with Bounded Risk in the Recapture Phase Under Inverse Binomial Sampling
Abstract
In the context of statistical ecology, a biologist may want to estimate the number of fish of certain species residing in a specific part of a large lake or an ocean. A forester working on behalf of the department of parks and wildlife may want to estimate how many deer are there in a large habitat. These are couple of motivating examples of importance where a common thread lies in the estimation of the size (N) of a closed and finite population. Estimation of a closed population size under inverse binomial sampling consists of four basic steps: First, one captures t items, then tag these t items, followed by releasing the t tagged items back to the population. Then, one draws an item from the population one-by-one until s tagged items are recaptured where s is fixed in advance. In the recapturing stage (fourth step), items are normally drawn with replacement. But, without replacement sampling will not impact much if N is large. Under squared error loss (SEL) as well as weighted SEL, we propose sequential methodologies to come up with bounded risk point estimators of an optimal choice of s; leading to an appropriate sequential estimator of N. The sequential estimation methodologies are supplemented with appropriate first-order asymptotic properties which are followed by extensive data analyses.
Keywords: Asymptotics; Bounded-risk; Capture; First-order properties; Recapture; Release; Risk; Sequential methodology; Squared error loss; Weighted squared error loss; Tagging.
DATE: Friday, April 12, 2019
TIME: 11:05 am
PLACE: Philip E. Austin Bldg., Rm. 434
Coffee will be served at 10:30 am in the Noether Lounge (AUST 326)
For more information, contact: Tracy Burke at tracy.burke@uconn.edu