On qualitative robustness of the Lotka-Nagaev estimator for the offspring mean of a supercritical Galton-Watson process
2016 | journal article. A publication with affiliation to the University of Göttingen.
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On qualitative robustness of the Lotka-Nagaev estimator for the offspring mean of a supercritical Galton-Watson process
Schuhmacher, D.; Sturm, A. & Zaehle, H. (2016)
Journal of Statistical Planning and Inference, 169 pp. 56-70. DOI: https://doi.org/10.1016/j.jspi.2015.08.003
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- Authors
- Schuhmacher, Dominic; Sturm, Anja ; Zaehle, Henryk
- Abstract
- We characterize the sets of offspring laws on which the Lotka-Nagaev estimator for the mean of a supercritical Galton-Watson process is qualitatively robust. These are exactly the locally uniformly integrating sets of offspring laws, which may be quite large. If the corresponding global property is assumed instead, we obtain uniform robustness as well. We illustrate both results with a number of concrete examples. As a by-product of the proof we obtain that the Lotka-Nagaev estimator is [locally] uniformly weakly consistent on the respective sets of offspring laws, conditionally on non-extinction. (C) 2015 Elsevier B.V. All rights reserved.
- Issue Date
- 2016
- Status
- published
- Publisher
- Elsevier Science Bv
- Journal
- Journal of Statistical Planning and Inference
- ISSN
- 1873-1171; 0378-3758