Beyond the delta method
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911831366303744 |
|---|---|
| author | Lejay, Antoine Mazzonetto, Sara |
| author_facet | Lejay, Antoine Mazzonetto, Sara |
| contents | We give an asymptotic development of the maximum likelihood estimator (MLE), or any other estimator defined implicitly, in a way which involves the limiting behavior of the score and its higher-order derivatives. This development, which is explicitly computable, gives some insights about the non-asymptotic behavior of the renormalized MLE and its departure from its limit. We highlight that the results hold whenever the score and its derivative converge, including to non Gaussian limits. Our approach is based on an asymptotic implicit function theorem, inspired from perturbative approaches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_13954 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Beyond the delta method Lejay, Antoine Mazzonetto, Sara Statistics Theory Probability Primary 62F12, Secondary 62F03, 62M02, 26B10 We give an asymptotic development of the maximum likelihood estimator (MLE), or any other estimator defined implicitly, in a way which involves the limiting behavior of the score and its higher-order derivatives. This development, which is explicitly computable, gives some insights about the non-asymptotic behavior of the renormalized MLE and its departure from its limit. We highlight that the results hold whenever the score and its derivative converge, including to non Gaussian limits. Our approach is based on an asymptotic implicit function theorem, inspired from perturbative approaches. |
| title | Beyond the delta method |
| topic | Statistics Theory Probability Primary 62F12, Secondary 62F03, 62M02, 26B10 |
| url | https://arxiv.org/abs/2207.13954 |