Cramér-Von Mises Statistic for Repeated Measures

• Main Authors: PABLO MARTÍNEZ-CAMBLOR, CARLOS CARLEOS, NORBERTO CORRAL
• Format: Article
• Language: English
• Published: Universidad Nacional de Colombia 2014-06-01
• Series: Revista Colombiana de Estadística
• Subjects: Bootstrap; distribución asintótica; estadístico de Cramér-von Mises; medidas repetidas; test de hipótesis; test de permutaciones
• Online Access: http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0120-17512014000100004&lng=en&tlng=en

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.