Information Bounds and Nonparametric Maximum Likelihood Estimation:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
1992
|
| Schriftenreihe: | DMV Seminar
19 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book contains the lecture notes for a DMV course presented by the authors at Gunzburg, Germany, in September, 1990. In the course we sketched the theory of information bounds for non parametric and semiparametric models, and developed the theory of non parametric maximum likelihood estimation in several particular inverse problems: interval censoring and deconvolution models. Part I, based on Jon Wellner's lectures, gives a brief sketch of information lower bound theory: Hajek's convolution theorem and extensions, useful minimax bounds for parametric problems due to Ibragimov and Has'minskii, and a recent result characterizing differentiable functionals due to van der Vaart (1991). The differentiability theorem is illustrated with the examples of interval censoring and deconvolution (which are pursued from the estimation perspective in part II). The differentiability theorem gives a way of clearly distinguishing situations in which 1 2 the parameter of interest can be estimated at rate n / and situations in which this is not the case. However it says nothing about which rates to expect when the functional is not differentiable. Even the casual reader will notice that several models are introduced, but not pursued in any detail; many problems remain. Part II, based on Piet Groeneboom's lectures, focuses on non parametric maximum likelihood estimates (NPMLE's) for certain inverse problems. The first chapter deals with the interval censoring problem |
| Beschreibung: | 1 Online-Ressource (VIII, 128 p) |
| ISBN: | 9783034886215 9783764327941 |
| DOI: | 10.1007/978-3-0348-8621-5 |
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Datensatz im Suchindex
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| discipline | Mathematik |
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| indexdate | 2024-07-10T01:21:10Z |
| institution | BVB |
| isbn | 9783034886215 9783764327941 |
| language | English |
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| spelling | Groeneboom, Piet Verfasser aut Information Bounds and Nonparametric Maximum Likelihood Estimation by Piet Groeneboom, Jon A. Wellner Basel Birkhäuser Basel 1992 1 Online-Ressource (VIII, 128 p) txt rdacontent c rdamedia cr rdacarrier DMV Seminar 19 This book contains the lecture notes for a DMV course presented by the authors at Gunzburg, Germany, in September, 1990. In the course we sketched the theory of information bounds for non parametric and semiparametric models, and developed the theory of non parametric maximum likelihood estimation in several particular inverse problems: interval censoring and deconvolution models. Part I, based on Jon Wellner's lectures, gives a brief sketch of information lower bound theory: Hajek's convolution theorem and extensions, useful minimax bounds for parametric problems due to Ibragimov and Has'minskii, and a recent result characterizing differentiable functionals due to van der Vaart (1991). The differentiability theorem is illustrated with the examples of interval censoring and deconvolution (which are pursued from the estimation perspective in part II). The differentiability theorem gives a way of clearly distinguishing situations in which 1 2 the parameter of interest can be estimated at rate n / and situations in which this is not the case. However it says nothing about which rates to expect when the functional is not differentiable. Even the casual reader will notice that several models are introduced, but not pursued in any detail; many problems remain. Part II, based on Piet Groeneboom's lectures, focuses on non parametric maximum likelihood estimates (NPMLE's) for certain inverse problems. The first chapter deals with the interval censoring problem Mathematics Mathematics, general Mathematik Semiparametrische Schätzung (DE-588)4232079-3 gnd rswk-swf Nichtparametrische Schätzung (DE-588)4203980-0 gnd rswk-swf Maximum-Likelihood-Schätzung (DE-588)4194624-8 gnd rswk-swf Maximum-Likelihood-Schätzung (DE-588)4194624-8 s 1\p DE-604 Semiparametrische Schätzung (DE-588)4232079-3 s 2\p DE-604 Nichtparametrische Schätzung (DE-588)4203980-0 s 3\p DE-604 Wellner, Jon A. Sonstige oth https://doi.org/10.1007/978-3-0348-8621-5 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Groeneboom, Piet Information Bounds and Nonparametric Maximum Likelihood Estimation Mathematics Mathematics, general Mathematik Semiparametrische Schätzung (DE-588)4232079-3 gnd Nichtparametrische Schätzung (DE-588)4203980-0 gnd Maximum-Likelihood-Schätzung (DE-588)4194624-8 gnd |
| subject_GND | (DE-588)4232079-3 (DE-588)4203980-0 (DE-588)4194624-8 |
| title | Information Bounds and Nonparametric Maximum Likelihood Estimation |
| title_auth | Information Bounds and Nonparametric Maximum Likelihood Estimation |
| title_exact_search | Information Bounds and Nonparametric Maximum Likelihood Estimation |
| title_full | Information Bounds and Nonparametric Maximum Likelihood Estimation by Piet Groeneboom, Jon A. Wellner |
| title_fullStr | Information Bounds and Nonparametric Maximum Likelihood Estimation by Piet Groeneboom, Jon A. Wellner |
| title_full_unstemmed | Information Bounds and Nonparametric Maximum Likelihood Estimation by Piet Groeneboom, Jon A. Wellner |
| title_short | Information Bounds and Nonparametric Maximum Likelihood Estimation |
| title_sort | information bounds and nonparametric maximum likelihood estimation |
| topic | Mathematics Mathematics, general Mathematik Semiparametrische Schätzung (DE-588)4232079-3 gnd Nichtparametrische Schätzung (DE-588)4203980-0 gnd Maximum-Likelihood-Schätzung (DE-588)4194624-8 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Semiparametrische Schätzung Nichtparametrische Schätzung Maximum-Likelihood-Schätzung |
| url | https://doi.org/10.1007/978-3-0348-8621-5 |
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