Barczy, Mátyás and Bojan, Basrak and Kevei, Péter and Pap, Gyula and Hrvoje, Planinić (2021) Statistical inference of subcritical strongly stationary Galton–Watson processes with regularly varying immigration. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 132. pp. 33-75. ISSN 0304-4149
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Abstract
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\in(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.
| Item Type: | Article |
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| Uncontrolled Keywords: | regularly varying distribution; Galton–Watson process with immigration; Conditional least squares estimator; Strong stationarity; Point process; |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 09 Jan 2023 11:43 |
| Last Modified: | 09 Jan 2023 11:43 |
| URI: | http://real.mtak.hu/id/eprint/156233 |
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