Optimal robust estimates using the Hellinger distance
Optimal robust M-estimates of a multidimensional parameter are described using Hampel's infinitesimal approach. The optimal estimates are derived by minimizing a measure of efficiency under the model, subject to a bounded measure of infinitesimal robustness. To this purpose we define measures o...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_18625347_v4_n2_p169_Marazzi |
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todo:paper_18625347_v4_n2_p169_Marazzi2023-10-03T16:33:24Z Optimal robust estimates using the Hellinger distance Marazzi, A. Yohai, V.J. gross error sensitivity Hampel's infinitesimal approach negative binomial distribution High energy physics Data sets Gross errors Hampel's infinitesimal approach Hellinger distance Kullback Leibler divergence Multi-dimensional parameters Negative binomial distribution Robust estimate Optimization Optimal robust M-estimates of a multidimensional parameter are described using Hampel's infinitesimal approach. The optimal estimates are derived by minimizing a measure of efficiency under the model, subject to a bounded measure of infinitesimal robustness. To this purpose we define measures of efficiency and infinitesimal sensitivity based on the Hellinger distance. We show that these two measures coincide with similar ones defined by Yohai using the Kullback-Leibler divergence, and therefore the corresponding optimal estimates coincide too. We also give an example where we fit a negative binomial distribution to a real dataset of "days of stay in hospital" using the optimal robust estimates. © 2010 Springer-Verlag. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_18625347_v4_n2_p169_Marazzi |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
gross error sensitivity Hampel's infinitesimal approach negative binomial distribution High energy physics Data sets Gross errors Hampel's infinitesimal approach Hellinger distance Kullback Leibler divergence Multi-dimensional parameters Negative binomial distribution Robust estimate Optimization |
| spellingShingle |
gross error sensitivity Hampel's infinitesimal approach negative binomial distribution High energy physics Data sets Gross errors Hampel's infinitesimal approach Hellinger distance Kullback Leibler divergence Multi-dimensional parameters Negative binomial distribution Robust estimate Optimization Marazzi, A. Yohai, V.J. Optimal robust estimates using the Hellinger distance |
| topic_facet |
gross error sensitivity Hampel's infinitesimal approach negative binomial distribution High energy physics Data sets Gross errors Hampel's infinitesimal approach Hellinger distance Kullback Leibler divergence Multi-dimensional parameters Negative binomial distribution Robust estimate Optimization |
| description |
Optimal robust M-estimates of a multidimensional parameter are described using Hampel's infinitesimal approach. The optimal estimates are derived by minimizing a measure of efficiency under the model, subject to a bounded measure of infinitesimal robustness. To this purpose we define measures of efficiency and infinitesimal sensitivity based on the Hellinger distance. We show that these two measures coincide with similar ones defined by Yohai using the Kullback-Leibler divergence, and therefore the corresponding optimal estimates coincide too. We also give an example where we fit a negative binomial distribution to a real dataset of "days of stay in hospital" using the optimal robust estimates. © 2010 Springer-Verlag. |
| format |
JOUR |
| author |
Marazzi, A. Yohai, V.J. |
| author_facet |
Marazzi, A. Yohai, V.J. |
| author_sort |
Marazzi, A. |
| title |
Optimal robust estimates using the Hellinger distance |
| title_short |
Optimal robust estimates using the Hellinger distance |
| title_full |
Optimal robust estimates using the Hellinger distance |
| title_fullStr |
Optimal robust estimates using the Hellinger distance |
| title_full_unstemmed |
Optimal robust estimates using the Hellinger distance |
| title_sort |
optimal robust estimates using the hellinger distance |
| url |
http://hdl.handle.net/20.500.12110/paper_18625347_v4_n2_p169_Marazzi |
| work_keys_str_mv |
AT marazzia optimalrobustestimatesusingthehellingerdistance AT yohaivj optimalrobustestimatesusingthehellingerdistance |
| _version_ |
1807322780073459712 |