Estimation in Semiparametric Models: Some Recent Developments
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer US
1990
|
| Series: | Lecture Notes in Statistics
63 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | Assume one has to estimate the mean J x P( dx) (or the median of P, or any other functional t;;(P)) on the basis ofi.i.d. observations from P. Ifnothing is known about P, then the sample mean is certainly the best estimator one can think of. If P is known to be the member of a certain parametric family, say {Po: {) E e}, one can usually do better by estimating {) first, say by {)(n)(.~.), and using J XPo(n)(;r.) (dx) as an estimate for J xPo(dx). There is an "intermediate" range, where we know something about the unknown probability measure P, but less than parametric theory takes for granted. Practical problems have always led statisticians to invent estimators for such intermediate models, but it usually remained open whether these estimators are nearly optimal or not. There was one exception: The case of "adaptivity", where a "nonparametric" estimate exists which is asymptotically optimal for any parametric submodel. The standard (and for a long time only) example of such a fortunate situation was the estimation of the center of symmetry for a distribution of unknown shape |
| Physical Description: | 1 Online-Ressource (III, 112p) |
| ISBN: | 9781461233961 9780387972381 |
| ISSN: | 0930-0325 |
| DOI: | 10.1007/978-1-4612-3396-1 |
Staff View
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| 500 | |a Assume one has to estimate the mean J x P( dx) (or the median of P, or any other functional t;;(P)) on the basis ofi.i.d. observations from P. Ifnothing is known about P, then the sample mean is certainly the best estimator one can think of. If P is known to be the member of a certain parametric family, say {Po: {) E e}, one can usually do better by estimating {) first, say by {)(n)(.~.), and using J XPo(n)(;r.) (dx) as an estimate for J xPo(dx). There is an "intermediate" range, where we know something about the unknown probability measure P, but less than parametric theory takes for granted. Practical problems have always led statisticians to invent estimators for such intermediate models, but it usually remained open whether these estimators are nearly optimal or not. There was one exception: The case of "adaptivity", where a "nonparametric" estimate exists which is asymptotically optimal for any parametric submodel. The standard (and for a long time only) example of such a fortunate situation was the estimation of the center of symmetry for a distribution of unknown shape | ||
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Record in the Search Index
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| author | Pfanzagl, Johann |
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| author_sort | Pfanzagl, Johann |
| author_variant | j p jp |
| building | Verbundindex |
| bvnumber | BV042420122 |
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| dewey-full | 519.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 |
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| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-3396-1 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T01:21:06Z |
| institution | BVB |
| isbn | 9781461233961 9780387972381 |
| issn | 0930-0325 |
| language | English |
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| spelling | Pfanzagl, Johann Verfasser aut Estimation in Semiparametric Models Some Recent Developments by Johann Pfanzagl New York, NY Springer US 1990 1 Online-Ressource (III, 112p) txt rdacontent c rdamedia cr rdacarrier Lecture Notes in Statistics 63 0930-0325 Assume one has to estimate the mean J x P( dx) (or the median of P, or any other functional t;;(P)) on the basis ofi.i.d. observations from P. Ifnothing is known about P, then the sample mean is certainly the best estimator one can think of. If P is known to be the member of a certain parametric family, say {Po: {) E e}, one can usually do better by estimating {) first, say by {)(n)(.~.), and using J XPo(n)(;r.) (dx) as an estimate for J xPo(dx). There is an "intermediate" range, where we know something about the unknown probability measure P, but less than parametric theory takes for granted. Practical problems have always led statisticians to invent estimators for such intermediate models, but it usually remained open whether these estimators are nearly optimal or not. There was one exception: The case of "adaptivity", where a "nonparametric" estimate exists which is asymptotically optimal for any parametric submodel. The standard (and for a long time only) example of such a fortunate situation was the estimation of the center of symmetry for a distribution of unknown shape Statistics Statistics, general Statistik Parameterschätzung (DE-588)4044614-1 gnd rswk-swf Semiparametrisches Modell (DE-588)4232479-8 gnd rswk-swf Schätzung (DE-588)4193791-0 gnd rswk-swf Semiparametrische Schätzung (DE-588)4232079-3 gnd rswk-swf Semiparametrisches Modell (DE-588)4232479-8 s Schätzung (DE-588)4193791-0 s 1\p DE-604 Parameterschätzung (DE-588)4044614-1 s 2\p DE-604 Semiparametrische Schätzung (DE-588)4232079-3 s 3\p DE-604 https://doi.org/10.1007/978-1-4612-3396-1 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 | Pfanzagl, Johann Estimation in Semiparametric Models Some Recent Developments Statistics Statistics, general Statistik Parameterschätzung (DE-588)4044614-1 gnd Semiparametrisches Modell (DE-588)4232479-8 gnd Schätzung (DE-588)4193791-0 gnd Semiparametrische Schätzung (DE-588)4232079-3 gnd |
| subject_GND | (DE-588)4044614-1 (DE-588)4232479-8 (DE-588)4193791-0 (DE-588)4232079-3 |
| title | Estimation in Semiparametric Models Some Recent Developments |
| title_auth | Estimation in Semiparametric Models Some Recent Developments |
| title_exact_search | Estimation in Semiparametric Models Some Recent Developments |
| title_full | Estimation in Semiparametric Models Some Recent Developments by Johann Pfanzagl |
| title_fullStr | Estimation in Semiparametric Models Some Recent Developments by Johann Pfanzagl |
| title_full_unstemmed | Estimation in Semiparametric Models Some Recent Developments by Johann Pfanzagl |
| title_short | Estimation in Semiparametric Models |
| title_sort | estimation in semiparametric models some recent developments |
| title_sub | Some Recent Developments |
| topic | Statistics Statistics, general Statistik Parameterschätzung (DE-588)4044614-1 gnd Semiparametrisches Modell (DE-588)4232479-8 gnd Schätzung (DE-588)4193791-0 gnd Semiparametrische Schätzung (DE-588)4232079-3 gnd |
| topic_facet | Statistics Statistics, general Statistik Parameterschätzung Semiparametrisches Modell Schätzung Semiparametrische Schätzung |
| url | https://doi.org/10.1007/978-1-4612-3396-1 |
| work_keys_str_mv | AT pfanzagljohann estimationinsemiparametricmodelssomerecentdevelopments |