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On a cramér‐von mises type statistic for testing bivariate independence
Author(s) -
Koziol James A.,
Nemec Amanda F.
Publication year - 1979
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315014
Subject(s) - bivariate analysis , mathematics , statistic , statistics , nonparametric statistics , independence (probability theory) , econometrics , rank (graph theory) , test statistic , statistical hypothesis testing , combinatorics
A Cramér‐von Mises type statistic for testing bivariate independence, proposed by Hoeffding (1948) and by Blum, Kiefer, and Rosenblatt (1961), is examined in greater detail. The statistic is decomposed into components in the manner of Durbin and Knott (1972), and the components are shown to be related to linear rank statistics. Asymptotic power properties of the Hoeffding statistic and its components in testing for independence with bivariate normal random observations are described; a Monte Carlo study comparing these statistics with other nonparametric statistics for bivariate independence is also reported.