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Activity Number: 36
Type: Contributed
Date/Time: Sunday, August 4, 2013 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract - #310307
Title: Joint Unified Confidence Region for the Parameters of Branching Processes with Immigration
Author(s): Pin Ren*+ and Anand Vidyashankar
Companies: and George Mason University
Keywords: branching processes ; empirical likelihood ; stopping time ; sequential analysis ; null-recurrent ; unified joint inference
Abstract:

Joint inference for the mean and variance parameters of branching processes is challenging due to the trichotomy exhibited by these processes. Empirical likelihood confidence region, when applied to such processes, cannot be calibrated using the chi-square distribution. We establish this rigorously and describe a novel methodology, using sequential analysis, that facilitates calibration using chi-squared distribution. In the process, we provide several interesting results concerning the rates of convergence of these processes. As a consequence of these rate results, we prove that for critical null-recurrent branching processes, the empirical likelihood converges in probability to zero. We illustrate our results with simulations and real-data examples.


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