Cramér-Von Mises Statistic for Repeated Measures
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| Natura: | Artículo científico |
| Lingua: | en |
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Universidad Nacional de Colombia
2014
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| _version_ | 1876488654395801600 |
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| author | Pablo Martínez-Camblor |
| author_facet | Pablo Martínez-Camblor |
| contents | Cramér-Von Mises Statistic for Repeated Measures Pablo Martínez-Camblor Carlos Carleos Norberto Corral Física, Astronomía y Matemáticas Cramér Bootstrap Permutation test Repeated Measures Hypothesis testing The Cramér-von Mises criterion is employed to compare whether the marginal distribution functions of a k-dimensional random variable are equal or not. The well-known Donsker invariance principle and the Karhunen- Loéve expansion is used in order to derive its asymptotic distribution. Two different resampling plans (one based on permutations and the other one based on the general bootstrap algorithm, gBA) are also considered to approximate its distribution. The practical behaviour of the proposed test is studied from a Monte Carlo simulation study. The statistical power of the test based on the Cramér-von Mises criterion is competitive when the underlying distributions are different in location and is clearly better than the Friedman one when the sole difference among the involved distributions is the spread or the shape. Both resampling plans lead to similar results although the gBA avoids the usual required interchangeability assumption. Finally, the method is applied on the study of the evolution inequality incomes distribution between some European countries along the years 2000 and 2011. 2014 artículo científico 0120-1751 https://www.redalyc.org/articulo.oa?id=89931327004 en http://www.redalyc.org/revista.oa?id=899 Revista Colombiana de Estadística application/pdf Universidad Nacional de Colombia Revista Colombiana de Estadística (Colombia) Num.1 Vol.37 |
| format | Artículo científico |
| id | redalyc_89931327004 |
| institution | Redalyc |
| language | en |
| publishDate | 2014 |
| publisher | Universidad Nacional de Colombia |
| spellingShingle | Cramér-Von Mises Statistic for Repeated Measures Pablo Martínez-Camblor Física, Astronomía y Matemáticas Cramér Bootstrap Permutation test Repeated Measures Hypothesis testing Cramér-Von Mises Statistic for Repeated Measures Pablo Martínez-Camblor Carlos Carleos Norberto Corral Física, Astronomía y Matemáticas Cramér Bootstrap Permutation test Repeated Measures Hypothesis testing The Cramér-von Mises criterion is employed to compare whether the marginal distribution functions of a k-dimensional random variable are equal or not. The well-known Donsker invariance principle and the Karhunen- Loéve expansion is used in order to derive its asymptotic distribution. Two different resampling plans (one based on permutations and the other one based on the general bootstrap algorithm, gBA) are also considered to approximate its distribution. The practical behaviour of the proposed test is studied from a Monte Carlo simulation study. The statistical power of the test based on the Cramér-von Mises criterion is competitive when the underlying distributions are different in location and is clearly better than the Friedman one when the sole difference among the involved distributions is the spread or the shape. Both resampling plans lead to similar results although the gBA avoids the usual required interchangeability assumption. Finally, the method is applied on the study of the evolution inequality incomes distribution between some European countries along the years 2000 and 2011. 2014 artículo científico 0120-1751 https://www.redalyc.org/articulo.oa?id=89931327004 en http://www.redalyc.org/revista.oa?id=899 Revista Colombiana de Estadística application/pdf Universidad Nacional de Colombia Revista Colombiana de Estadística (Colombia) Num.1 Vol.37 |
| title | Cramér-Von Mises Statistic for Repeated Measures |
| topic | Física, Astronomía y Matemáticas Cramér Bootstrap Permutation test Repeated Measures Hypothesis testing |
| url | https://www.redalyc.org/articulo.oa?id=89931327004 |