Two Bootstrap Strategies for a k-Problem up to Location-Scale with Dependent Samples
This paper extends the work of Quessy and Éthier (2012) who considered tests for the k-sample problem with dependent samples. Here, the marginal distributions are allowed, under H0, to differ according to their mean and their variance; in other words, one focuses on the shape of the distributions. A...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2014/523139 |
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| _version_ | 1832553218246180864 |
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| author | Jean-François Quessy François Éthier |
| author_facet | Jean-François Quessy François Éthier |
| author_sort | Jean-François Quessy |
| collection | DOAJ |
| description | This paper extends the work of Quessy and Éthier (2012) who considered tests for the k-sample problem with dependent samples. Here, the marginal distributions are allowed, under H0, to differ according to their mean and their variance; in other words, one focuses on the shape of the distributions. Although easily stated, this problem nevertheless requires a careful treatment for the computation of valid P values. To this end, two bootstrap strategies based on the multiplier central limit theorem are proposed, both exploiting a representation of the test statistics in terms of a Hadamard differentiable functional. This accounts for the fact that one works with empirically standardized data instead of the original observations. Simulations reported show the nice sample properties of the method based on Cramér-von Mises and characteristic function type statistics. The newly introduced tests are illustrated on the marginal distributions of the eight-dimensional Oil currency data set. |
| format | Article |
| id | doaj-art-b0c7b3a6e3b749f3b0a9cbe25a70dbbb |
| institution | Kabale University |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-b0c7b3a6e3b749f3b0a9cbe25a70dbbb2025-02-03T05:55:16ZengWileyJournal of Probability and Statistics1687-952X1687-95382014-01-01201410.1155/2014/523139523139Two Bootstrap Strategies for a k-Problem up to Location-Scale with Dependent SamplesJean-François Quessy0François Éthier1Département de Mathématiques et d'Informatique, Université du Québec à Trois-Rivières, Trois-Rivières, QC, G9A 5H7, CanadaDépartement de Mathématiques et d'Informatique, Université du Québec à Trois-Rivières, Trois-Rivières, QC, G9A 5H7, CanadaThis paper extends the work of Quessy and Éthier (2012) who considered tests for the k-sample problem with dependent samples. Here, the marginal distributions are allowed, under H0, to differ according to their mean and their variance; in other words, one focuses on the shape of the distributions. Although easily stated, this problem nevertheless requires a careful treatment for the computation of valid P values. To this end, two bootstrap strategies based on the multiplier central limit theorem are proposed, both exploiting a representation of the test statistics in terms of a Hadamard differentiable functional. This accounts for the fact that one works with empirically standardized data instead of the original observations. Simulations reported show the nice sample properties of the method based on Cramér-von Mises and characteristic function type statistics. The newly introduced tests are illustrated on the marginal distributions of the eight-dimensional Oil currency data set.http://dx.doi.org/10.1155/2014/523139 |
| spellingShingle | Jean-François Quessy François Éthier Two Bootstrap Strategies for a k-Problem up to Location-Scale with Dependent Samples Journal of Probability and Statistics |
| title | Two Bootstrap Strategies for a k-Problem up to Location-Scale with Dependent Samples |
| title_full | Two Bootstrap Strategies for a k-Problem up to Location-Scale with Dependent Samples |
| title_fullStr | Two Bootstrap Strategies for a k-Problem up to Location-Scale with Dependent Samples |
| title_full_unstemmed | Two Bootstrap Strategies for a k-Problem up to Location-Scale with Dependent Samples |
| title_short | Two Bootstrap Strategies for a k-Problem up to Location-Scale with Dependent Samples |
| title_sort | two bootstrap strategies for a k problem up to location scale with dependent samples |
| url | http://dx.doi.org/10.1155/2014/523139 |
| work_keys_str_mv | AT jeanfrancoisquessy twobootstrapstrategiesforakproblemuptolocationscalewithdependentsamples AT francoisethier twobootstrapstrategiesforakproblemuptolocationscalewithdependentsamples |