Journal
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
Volume 132, Issue -, Pages 33-75Publisher
ELSEVIER
DOI: 10.1016/j.spa.2020.10.004
Keywords
Galton-Watson process with immigration; Conditional least squares estimator; Regularly varying distribution; Strong stationarity; Point process
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Funding
- Hungarian Croatian Intergovernmental S&T Cooperation Programme [16-1-2016-0027]
- Janos Bolyai Research Scholarship of the Hungarian Academy of Sciences
- Croatian-Swiss Research Program of the Croatian Science Foundation
- Swiss National Science Foundation [CSRP 018-01-180549]
- Ministry for Innovation and Technology, Hungary [TUDFO/47138-1/2019-ITM]
- EU [EFOP-3.6.1-16-2016-00008]
- NKFIH grant [FK124141]
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This paper focuses on the asymptotic behavior of the conditional least squares estimator of the offspring mean for subcritical strongly stationary Galton-Watson processes with regularly varying immigration. The limit law is the ratio of two dependent stable random variables with specific indices, and it has a continuously differentiable density function. Point process technique is used in the proofs.
We describe the asymptotic behavior of the conditional least squares estimator of the offspring mean for subcritical strongly stationary Galton-Watson processes with regularly varying immigration with tail index alpha is an element of (1, 2). The limit law is the ratio of two dependent stable random variables with indices alpha/2 and 2 alpha/3, respectively, and it has a continuously differentiable density function. We use point process technique in the proofs. (C) 2020 The Author(s). Published by Elsevier B.V.
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