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Large Sample Inference for Markovian Exponential Families with Application to Branching Processes with Immigration
Author(s) -
Hudson Irene L.
Publication year - 1982
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1982.tb00811.x
Subject(s) - exponential family , branching process , statistical physics , mathematics , statistic , inference , phase type distribution , econometrics , markov process , statistics , computer science , physics , artificial intelligence
Summary 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.