Rates of convergence for partial mass problems
We consider a class of partial mass problems in which a fraction of the mass of a probability measure is allowed to be changed (trimmed) to maximize fit to a given pattern. This includes the problem of optimal partial transportation of mass, where a part of the mass need not be transported, and also...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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2013
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| _version_ | 1826272845413482496 |
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| author | del Barrio, E Matrán, C |
| author_facet | del Barrio, E Matrán, C |
| author_sort | del Barrio, E |
| collection | OXFORD |
| description | We consider a class of partial mass problems in which a fraction of the mass of a probability measure is allowed to be changed (trimmed) to maximize fit to a given pattern. This includes the problem of optimal partial transportation of mass, where a part of the mass need not be transported, and also trimming procedures which are often used in statistical data analysis to discard outliers in a sample (the data with lowest agreement to a certain pattern). This results in a modified, trimmed version of the original probability which is closer to the pattern. We focus on the case of the empirical measure and analyze to what extent its optimally trimmed version is closer to the true random generator in terms of rates of convergence. We deal with probabilities on ℝk and measure agreement through probability metrics. Our choices include transportation cost metrics, associated to optimal partial transportation, and the Kolmogorov distance. We show that partial transportation (as opposed to classical, complete transportation) results in a sharp decrease of costs only in low dimension. In contrast, for the Kolmogorov metric this decrease is seen in any dimension. © 2011 Springer-Verlag. |
| first_indexed | 2024-03-06T22:19:01Z |
| format | Journal article |
| id | oxford-uuid:5464cd81-4294-4de7-b551-803b00cec20d |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T22:19:01Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | oxford-uuid:5464cd81-4294-4de7-b551-803b00cec20d2022-03-26T16:37:33ZRates of convergence for partial mass problemsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:5464cd81-4294-4de7-b551-803b00cec20dEnglishSymplectic Elements at Oxford2013del Barrio, EMatrán, CWe consider a class of partial mass problems in which a fraction of the mass of a probability measure is allowed to be changed (trimmed) to maximize fit to a given pattern. This includes the problem of optimal partial transportation of mass, where a part of the mass need not be transported, and also trimming procedures which are often used in statistical data analysis to discard outliers in a sample (the data with lowest agreement to a certain pattern). This results in a modified, trimmed version of the original probability which is closer to the pattern. We focus on the case of the empirical measure and analyze to what extent its optimally trimmed version is closer to the true random generator in terms of rates of convergence. We deal with probabilities on ℝk and measure agreement through probability metrics. Our choices include transportation cost metrics, associated to optimal partial transportation, and the Kolmogorov distance. We show that partial transportation (as opposed to classical, complete transportation) results in a sharp decrease of costs only in low dimension. In contrast, for the Kolmogorov metric this decrease is seen in any dimension. © 2011 Springer-Verlag. |
| spellingShingle | del Barrio, E Matrán, C Rates of convergence for partial mass problems |
| title | Rates of convergence for partial mass problems |
| title_full | Rates of convergence for partial mass problems |
| title_fullStr | Rates of convergence for partial mass problems |
| title_full_unstemmed | Rates of convergence for partial mass problems |
| title_short | Rates of convergence for partial mass problems |
| title_sort | rates of convergence for partial mass problems |
| work_keys_str_mv | AT delbarrioe ratesofconvergenceforpartialmassproblems AT matranc ratesofconvergenceforpartialmassproblems |