Optimal Estimators for Threshold-Based Quality Measures
We consider a problem in parametric estimation: given n samples from an unknown distribution, we want to estimate which distribution, from a given one-parameter family, produced the data. Following Schulman and Vazirani (2005), we evaluate an estimator in terms of the chance of being within a specif...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2010/752750 |
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| _version_ | 1832559442235752448 |
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| author | Aaron Abrams Sandy Ganzell Henry Landau Zeph Landau James Pommersheim Eric Zaslow |
| author_facet | Aaron Abrams Sandy Ganzell Henry Landau Zeph Landau James Pommersheim Eric Zaslow |
| author_sort | Aaron Abrams |
| collection | DOAJ |
| description | We consider a problem in parametric estimation: given n samples from an unknown distribution, we want to estimate which distribution, from a given one-parameter family, produced the data. Following Schulman and Vazirani (2005), we evaluate an estimator in terms
of the chance of being within a specified tolerance of the correct answer,
in the worst case. We provide optimal estimators for several families of
distributions on ℝ. We prove that for distributions on a compact space,
there is always an optimal estimator that is translation invariant, and
we conjecture that this conclusion also holds for any distribution on ℝ.
By contrast, we give an example showing that, it does not hold for a certain
distribution on an infinite tree. |
| format | Article |
| id | doaj-art-bbfbe9be2d504e15a6ada043e0b5d6b5 |
| institution | Kabale University |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-bbfbe9be2d504e15a6ada043e0b5d6b52025-02-03T01:30:09ZengWileyJournal of Probability and Statistics1687-952X1687-95382010-01-01201010.1155/2010/752750752750Optimal Estimators for Threshold-Based Quality MeasuresAaron Abrams0Sandy Ganzell1Henry Landau2Zeph Landau3James Pommersheim4Eric Zaslow5Department of Mathematics and Computer Science, Emory University, USADepartment of Mathematics and Computer Science, St. Mary’s College of Maryland, USAAT&T Research, USADepartment of Computer Science, University of California, Berkeley, USAJames Pommersheim, Department of Mathematics, Reed College, USADepartment of Mathematics, Northwestern University, USAWe consider a problem in parametric estimation: given n samples from an unknown distribution, we want to estimate which distribution, from a given one-parameter family, produced the data. Following Schulman and Vazirani (2005), we evaluate an estimator in terms of the chance of being within a specified tolerance of the correct answer, in the worst case. We provide optimal estimators for several families of distributions on ℝ. We prove that for distributions on a compact space, there is always an optimal estimator that is translation invariant, and we conjecture that this conclusion also holds for any distribution on ℝ. By contrast, we give an example showing that, it does not hold for a certain distribution on an infinite tree.http://dx.doi.org/10.1155/2010/752750 |
| spellingShingle | Aaron Abrams Sandy Ganzell Henry Landau Zeph Landau James Pommersheim Eric Zaslow Optimal Estimators for Threshold-Based Quality Measures Journal of Probability and Statistics |
| title | Optimal Estimators for Threshold-Based Quality Measures |
| title_full | Optimal Estimators for Threshold-Based Quality Measures |
| title_fullStr | Optimal Estimators for Threshold-Based Quality Measures |
| title_full_unstemmed | Optimal Estimators for Threshold-Based Quality Measures |
| title_short | Optimal Estimators for Threshold-Based Quality Measures |
| title_sort | optimal estimators for threshold based quality measures |
| url | http://dx.doi.org/10.1155/2010/752750 |
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