Censored lifespans in a double-truncated sample: Maximum likelihood inference for the exponential distribution
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912532147470336 |
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| author | Sieg, Fiete Toparkus, Anne-Marie Weissbach, Rafael |
| author_facet | Sieg, Fiete Toparkus, Anne-Marie Weissbach, Rafael |
| contents | The analysis of a truncated sample can be hindered by censoring. Survival information may be lost to follow-up or the birthdate may be missing. The data can still be modeled as a truncated point process and it is close to a Poisson process, in the Hellinger distance, as long as the sample is small relative to the population. We assume an exponential distribution for the lifespan, derive the likelihood and profile out the unobservable sample size. Identification of the exponential parameter is shown, together with consistency and asymptotic normality of its M-estimator. Even though the estimator sequence is indexed in the sample size, both the point estimator and the standard error are observable. Enterprise lifespans in Germany constitute our example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_16623 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Censored lifespans in a double-truncated sample: Maximum likelihood inference for the exponential distribution Sieg, Fiete Toparkus, Anne-Marie Weissbach, Rafael Methodology 62N01, 62D10, 60G55 G.3; I.5.2 The analysis of a truncated sample can be hindered by censoring. Survival information may be lost to follow-up or the birthdate may be missing. The data can still be modeled as a truncated point process and it is close to a Poisson process, in the Hellinger distance, as long as the sample is small relative to the population. We assume an exponential distribution for the lifespan, derive the likelihood and profile out the unobservable sample size. Identification of the exponential parameter is shown, together with consistency and asymptotic normality of its M-estimator. Even though the estimator sequence is indexed in the sample size, both the point estimator and the standard error are observable. Enterprise lifespans in Germany constitute our example. |
| title | Censored lifespans in a double-truncated sample: Maximum likelihood inference for the exponential distribution |
| topic | Methodology 62N01, 62D10, 60G55 G.3; I.5.2 |
| url | https://arxiv.org/abs/2504.16623 |