Asymptotic efficiency of statistical estimators: concepts and higher order asymptotic efficiency
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1981
|
| Schriftenreihe: | Lecture Notes in Statistics
7 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This monograph is a collection of results recently obtained by the authors. Most of these have been published, while others are awaitlng publication. Our investigation has two main purposes. Firstly, we discuss higher order asymptotic efficiency of estimators in regular situations. In these situations it is known that the maximum likelihood estimator (MLE) is asymptotically efficient in some (not always specified) sense. However, there exists here a whole class of asymptotically efficient estimators which are thus asymptotically equivalent to the MLE. It is required to make finer distinctions among the estimators, by considering higher order terms in the expansions of their asymptotic distributions. Secondly, we discuss asymptotically efficient estimators in nonregular situations. These are situations where the MLE or other estimators are not asymptotically normally distributed, or where l 2 their order of convergence (or consistency) is not n / , as in the regular cases. It is necessary to redefine the concept of asymptotic efficiency, together with the concept of the maximum order of consistency. Under the new definition as asymptotically efficient estimator may not always exist. We have not attempted to tell the whole story in a systematic way. The field of asymptotic theory in statistical estimation is relatively uncultivated. So, we have tried to focus attention on such aspects of our recent results which throw light on the area |
| Beschreibung: | 1 Online-Ressource (242p) |
| ISBN: | 9781461259275 9780387905761 |
| ISSN: | 0930-0325 |
| DOI: | 10.1007/978-1-4612-5927-5 |
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| id | DE-604.BV042420435 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-20T06:44:52Z |
| institution | BVB |
| isbn | 9781461259275 9780387905761 |
| issn | 0930-0325 |
| language | English |
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| series2 | Lecture Notes in Statistics |
| spelling | Akahira, Masafumi 1945- Verfasser (DE-588)1089239793 aut Asymptotic efficiency of statistical estimators concepts and higher order asymptotic efficiency by Masafumi Akahira, Kei Takeuchi New York, NY Springer New York 1981 1 Online-Ressource (242p) txt rdacontent c rdamedia cr rdacarrier Lecture Notes in Statistics 7 0930-0325 This monograph is a collection of results recently obtained by the authors. Most of these have been published, while others are awaitlng publication. Our investigation has two main purposes. Firstly, we discuss higher order asymptotic efficiency of estimators in regular situations. In these situations it is known that the maximum likelihood estimator (MLE) is asymptotically efficient in some (not always specified) sense. However, there exists here a whole class of asymptotically efficient estimators which are thus asymptotically equivalent to the MLE. It is required to make finer distinctions among the estimators, by considering higher order terms in the expansions of their asymptotic distributions. Secondly, we discuss asymptotically efficient estimators in nonregular situations. These are situations where the MLE or other estimators are not asymptotically normally distributed, or where l 2 their order of convergence (or consistency) is not n / , as in the regular cases. It is necessary to redefine the concept of asymptotic efficiency, together with the concept of the maximum order of consistency. Under the new definition as asymptotically efficient estimator may not always exist. We have not attempted to tell the whole story in a systematic way. The field of asymptotic theory in statistical estimation is relatively uncultivated. So, we have tried to focus attention on such aspects of our recent results which throw light on the area Statistics Statistics, general Statistik Takeuchi, Kei 1933- Sonstige (DE-588)170069389 oth Lecture Notes in Statistics 7 (DE-604)BV036592911 7 https://doi.org/10.1007/978-1-4612-5927-5 Verlag Volltext |
| spellingShingle | Akahira, Masafumi 1945- Asymptotic efficiency of statistical estimators concepts and higher order asymptotic efficiency Lecture Notes in Statistics Statistics Statistics, general Statistik |
| title | Asymptotic efficiency of statistical estimators concepts and higher order asymptotic efficiency |
| title_auth | Asymptotic efficiency of statistical estimators concepts and higher order asymptotic efficiency |
| title_exact_search | Asymptotic efficiency of statistical estimators concepts and higher order asymptotic efficiency |
| title_full | Asymptotic efficiency of statistical estimators concepts and higher order asymptotic efficiency by Masafumi Akahira, Kei Takeuchi |
| title_fullStr | Asymptotic efficiency of statistical estimators concepts and higher order asymptotic efficiency by Masafumi Akahira, Kei Takeuchi |
| title_full_unstemmed | Asymptotic efficiency of statistical estimators concepts and higher order asymptotic efficiency by Masafumi Akahira, Kei Takeuchi |
| title_short | Asymptotic efficiency of statistical estimators |
| title_sort | asymptotic efficiency of statistical estimators concepts and higher order asymptotic efficiency |
| title_sub | concepts and higher order asymptotic efficiency |
| topic | Statistics Statistics, general Statistik |
| topic_facet | Statistics Statistics, general Statistik |
| url | https://doi.org/10.1007/978-1-4612-5927-5 |
| volume_link | (DE-604)BV036592911 |
| work_keys_str_mv | AT akahiramasafumi asymptoticefficiencyofstatisticalestimatorsconceptsandhigherorderasymptoticefficiency AT takeuchikei asymptoticefficiencyofstatisticalestimatorsconceptsandhigherorderasymptoticefficiency |