Consistent procedures for multiclass classification of discrete diffusion paths
The recent advent of modern technology has generated a large number of datasets which can be frequently modeled as functional data. This paper focuses on the problem of multiclass classification for stochastic diffusion paths. In this context we establish a closed formula for the optimal Bayes rule....
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| Published in | Scandinavian journal of statistics Vol. 47; no. 2; pp. 516 - 554 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Oxford
Blackwell Publishing Ltd
01.06.2020
Wiley |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0303-6898 1467-9469 |
| DOI | 10.1111/sjos.12415 |
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| Abstract | The recent advent of modern technology has generated a large number of datasets which can be frequently modeled as functional data. This paper focuses on the problem of multiclass classification for stochastic diffusion paths. In this context we establish a closed formula for the optimal Bayes rule. We provide new statistical procedures which are built either on the plug‐in principle or on the empirical risk minimization principle. We show the consistency of these procedures under mild conditions. We apply our methodologies to the parametric case and illustrate their accuracy with a simulation study through examples. |
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| AbstractList | The recent advent of modern technology has generated a large number of datasets which can be frequently modeled as functional data. This paper focuses on the problem of multiclass classification for stochastic diffusion paths. In this context we establish a closed formula for the optimal Bayes rule. We provide new statistical procedures which are built either on the plug‐in principle or on the empirical risk minimization principle. We show the consistency of these procedures under mild conditions. We apply our methodologies to the parametric case and illustrate their accuracy with a simulation study through examples. The recent advent of modern technology has generated a large number of datasets which can be frequently modeled as functional data. This paper focuses on the problem of multiclass classification for stochastic diffusion paths. In this context we establish a closed formula for the optimal Bayes rule. We provide new statistical procedures which are built either on the plug‐in principle or on the empirical risk minimization principle. We show the consistency of these procedures under mild conditions. We apply our methodologies to the parametric case and illustrate their accuracy with a simulation study through examples. |
| Author | Denis, Christophe Martinez, Miguel Dion, Charlotte |
| Author_xml | – sequence: 1 givenname: Christophe orcidid: 0000-0002-9424-1811 surname: Denis fullname: Denis, Christophe email: christophe.denis@u-pem.fr organization: Université Paris Est Marne‐la‐Vallée – sequence: 2 givenname: Charlotte surname: Dion fullname: Dion, Charlotte organization: Sorbonne Université – sequence: 3 givenname: Miguel surname: Martinez fullname: Martinez, Miguel organization: Université Paris Est Marne‐la‐Vallée |
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| Keywords | plug-in estimators diffusion paths 62H30 empirical risk minimization AMS Subject Classification: 62M05 62F12 empirical risk minimization Multiclass classification drift estimation |
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| SubjectTerms | Classification Computer simulation diffusion paths drift estimation multiclass classification Optimization plug‐in estimators Statistics Statistics Theory |
| Title | Consistent procedures for multiclass classification of discrete diffusion paths |
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