Existence and non-existence of consistent estimators in supercritical controlled branching processes
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918126199767040 |
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| author | Braunsteins, Peter Hautphenne, Sophie Kerlidis, James |
| author_facet | Braunsteins, Peter Hautphenne, Sophie Kerlidis, James |
| contents | We consider the problem of estimating the parameters of a supercritical controlled branching process consistently from a single observed trajectory of population size counts. Our goal is to establish which parameters can and cannot be consistently estimated. When a parameter can be consistently estimated, we derive an explicit expression for the estimator. We address these questions in three scenarios: when the distribution of the control function distribution is known, when it is unknown, and when progenitor numbers are observed alongside population size counts. Our results offer a theoretical justification for the common practice in population ecology of estimating demographic and environmental stochasticity using separate observation schemes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_03389 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence and non-existence of consistent estimators in supercritical controlled branching processes Braunsteins, Peter Hautphenne, Sophie Kerlidis, James Probability Statistics Theory 60J80 We consider the problem of estimating the parameters of a supercritical controlled branching process consistently from a single observed trajectory of population size counts. Our goal is to establish which parameters can and cannot be consistently estimated. When a parameter can be consistently estimated, we derive an explicit expression for the estimator. We address these questions in three scenarios: when the distribution of the control function distribution is known, when it is unknown, and when progenitor numbers are observed alongside population size counts. Our results offer a theoretical justification for the common practice in population ecology of estimating demographic and environmental stochasticity using separate observation schemes. |
| title | Existence and non-existence of consistent estimators in supercritical controlled branching processes |
| topic | Probability Statistics Theory 60J80 |
| url | https://arxiv.org/abs/2504.03389 |