On the Parametric Maximum Likelihood Estimator for Independent but Non-identically Distributed Observations with Application to Truncated Data
We investigate the parametric maximum likelihood estimator for truncated data when the truncation value is different according to the observed individual or item. We extend Lehmann’s proof (1983) of the asymptotic properties of the parametric maximum likelihood estimator in the case of independent n...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Springer
2016-02-01
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| Series: | Journal of Statistical Theory and Applications (JSTA) |
| Subjects: | |
| Online Access: | https://www.atlantis-press.com/article/25850503.pdf |
| _version_ | 1811302427835498496 |
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| author | Fanny Leroy Jean-Yves Dauxois Pascale Tubert-Bitter |
| author_facet | Fanny Leroy Jean-Yves Dauxois Pascale Tubert-Bitter |
| author_sort | Fanny Leroy |
| collection | DOAJ |
| description | We investigate the parametric maximum likelihood estimator for truncated data when the truncation value is different according to the observed individual or item. We extend Lehmann’s proof (1983) of the asymptotic properties of the parametric maximum likelihood estimator in the case of independent nonidentically distributed observations. Two cases are considered: either the number of distinct probability distribution functions that can be observed in the population from which the sample comes from is finite or this number is infinite. Sufficient conditions for consistency and asymptotic normality are provided for both cases. |
| first_indexed | 2024-04-13T07:27:41Z |
| format | Article |
| id | doaj.art-4308de08c61147929d61605931902271 |
| institution | Directory Open Access Journal |
| issn | 1538-7887 |
| language | English |
| last_indexed | 2024-04-13T07:27:41Z |
| publishDate | 2016-02-01 |
| publisher | Springer |
| record_format | Article |
| series | Journal of Statistical Theory and Applications (JSTA) |
| spelling | doaj.art-4308de08c61147929d616059319022712022-12-22T02:56:26ZengSpringerJournal of Statistical Theory and Applications (JSTA)1538-78872016-02-0115110.2991/jsta.2016.15.1.8On the Parametric Maximum Likelihood Estimator for Independent but Non-identically Distributed Observations with Application to Truncated DataFanny LeroyJean-Yves DauxoisPascale Tubert-BitterWe investigate the parametric maximum likelihood estimator for truncated data when the truncation value is different according to the observed individual or item. We extend Lehmann’s proof (1983) of the asymptotic properties of the parametric maximum likelihood estimator in the case of independent nonidentically distributed observations. Two cases are considered: either the number of distinct probability distribution functions that can be observed in the population from which the sample comes from is finite or this number is infinite. Sufficient conditions for consistency and asymptotic normality are provided for both cases.https://www.atlantis-press.com/article/25850503.pdfParametric maximum likelihood estimator; Independent non-identically distributed observations; Consistency; Asymptotic normality; Truncated data. |
| spellingShingle | Fanny Leroy Jean-Yves Dauxois Pascale Tubert-Bitter On the Parametric Maximum Likelihood Estimator for Independent but Non-identically Distributed Observations with Application to Truncated Data Journal of Statistical Theory and Applications (JSTA) Parametric maximum likelihood estimator; Independent non-identically distributed observations; Consistency; Asymptotic normality; Truncated data. |
| title | On the Parametric Maximum Likelihood Estimator for Independent but Non-identically Distributed Observations with Application to Truncated Data |
| title_full | On the Parametric Maximum Likelihood Estimator for Independent but Non-identically Distributed Observations with Application to Truncated Data |
| title_fullStr | On the Parametric Maximum Likelihood Estimator for Independent but Non-identically Distributed Observations with Application to Truncated Data |
| title_full_unstemmed | On the Parametric Maximum Likelihood Estimator for Independent but Non-identically Distributed Observations with Application to Truncated Data |
| title_short | On the Parametric Maximum Likelihood Estimator for Independent but Non-identically Distributed Observations with Application to Truncated Data |
| title_sort | on the parametric maximum likelihood estimator for independent but non identically distributed observations with application to truncated data |
| topic | Parametric maximum likelihood estimator; Independent non-identically distributed observations; Consistency; Asymptotic normality; Truncated data. |
| url | https://www.atlantis-press.com/article/25850503.pdf |
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