Summary
Estimation theory for the variances of the offspring and immigration distributions in a simple branching process with immigration is developed, analogous to the estimation theory for the means given by Wei and Winnicki (1990). Conditional and weighted conditional least squares estimators are considered and their asymptotic properties for the full range of parameters are studied. Nonexistence of consistent estimators in the critical case is established, which complements analogous result of Wei and Winnicki for the supercritical case.
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Research supported by the National Science Foundation under Grant NSF-DMS-8801496
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Winnicki, J. Estimation of the variances in the branching process with immigration. Probab. Th. Rel. Fields 88, 77–106 (1991). https://doi.org/10.1007/BF01193583
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DOI: https://doi.org/10.1007/BF01193583