http://dx.doi.org/10.15446/rce.v37n1.44357

¹FICYT, Oficina de Investigación Biosanitaria (OIB), Oviedo, Spain. Universidad de Oviedo, Departamento Estadística e IO y DM, Asturias, Spain. Biostatistician. Email: pmcamblor@hotmail.com
²Universidad de Oviedo, Departamento Estadística e IO y DM, Asturias, Spain. Professor. Email: carleos@uniovi.es
³Universidad de Oviedo, Departamento Estadística e IO y DM, Asturias, Spain. Lecturer. Email: norbert@uniovi.es

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.

Key words: Asymptotic Distribution, Bootstrap, Cramér-von Mises statistic, Hypothesis testing, Permutation test, Repeated Measures.

El criterio de Cramér-von Mises es empleado para comparar la igualdad entre las distribuciones marginales de una variable aleatoria k-dimensional. El conocido principio de invaranza de Donsker y la expansión de Karhunen-Loéve se usan para derivar su distribución asintótica. Dos planes de remuestreo diferentes (uno basado en permutaciones y el otro basado en el algoritmo bootstrap general, gBA) son usados para aproximar su distribución. El comportamiento práctico del test propuesto es estudiado mediante simulaciones de Monte Carlo. La potencia estadística del test basado en el criterio de Cramér-von Mises es competitiva cuando la distribuciones subyacentes difieren en el parámetro de localización. Este test es claramente superior al de Friedman cuando las únicas diferencias son en la dispersión o la forma. Ambos planes de remuestreo obtienen resultados similares aunque el gBA evita la hipótesis de intercambiabilidad. Finalmente, el método propuesto es aplicado al estudio de la evolución de las desigualdades en los ingresos entre algunos países Europeos entre los años 2000 y 2011.

Palabras clave: Bootstrap, distribución asintótica, estadístico de Cramér-von Mises, medidas repetidas, test de hipótesis, test de permutaciones.

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