On the Cramér–Von Mises Statistic

Probably, one of the most useful criterions in order to compare distribution functions is the one introduced by the researchers Harald Cramér and Richard Edler von Mises which is known as Cramérvon Mises criterion $(C_M)$. It has been applied on a vast variety of problems. In this work, the theory o...

Full description

Main Authors: Martínez Camblor, Pablo, Carleos, Carlos, Corral, Norberto
Format: Artículo
Language: Español
Published: 2015
Online Access: http://revistas.ucr.ac.cr/index.php/matematica/article/view/2107
http://hdl.handle.net/10669/13009
Summary: Probably, one of the most useful criterions in order to compare distribution functions is the one introduced by the researchers Harald Cramér and Richard Edler von Mises which is known as Cramérvon Mises criterion $(C_M)$. It has been applied on a vast variety of problems. In this work, the theory of empirical processes is applied in order to obtain the asymptotic distribution for the generalization to the k-sample problem of $(C_M)$ proposed by Kiefer. The quality of this approximation is also studied and some indications about how to obtain an approximation to the final P-value are also included.