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Large Sample Inference for Markovian Exponential Families with Application to Branching Processes with Immigration |
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| Authors: | Irene L. Hudson |
| Affiliation: | La Trobe University |
| Abstract: | This paper presents limit distributions for the score and likelihood-ratio (L.R.) statistic for testing a composite hypothesis involving the mean of the offspring distribution of the Bienaymé-Galton-Watson branching process with immigration (BPWI) when the process is subcritical, critical or supercritical. The BPWI is shown to be a member of a certain Markovian exponential family. |
| Keywords: | Asymptotic theory Markovian exponential families Composite hypothesis Score test statistic Likelihood-ratio statistic Branching process with immigration |