Asymptotic local efficiency of Cramér–von Mises tests for multivariate independence

Deheuvels [J. Multivariate Anal. 11 (1981) 102-113] and Genest and Remillard [Test 13 (2004) 335-369] have shown that powerful rank tests of multivariate independence can be based on combinations of asymptotically independent Cramer-von Mises statistics derived from a Mobius decomposition of the empirical copula process. A result on the large-sample behavior of this process under contiguous sequences of alternatives is used here to give a representation of the limiting distribution of such test statistics and to compute their relative local asymptotic efficiency. Local power curves and asymptotic relative efficiencies are compared under familiar classes of copula alternatives.

[1]  Bruno Rémillard,et al.  Local efficiency of a Cramér--von Mises test of independence , 2005 .

[2]  B. Rémillard,et al.  Test of independence and randomness based on the empirical copula process , 2004 .

[3]  B. Rémillard,et al.  Tests of Independence Based on the Empirical Copula Process , 2003 .

[4]  B. Rémillard,et al.  A Nonparametric Test of Serial Independence for Time Series and Residuals , 2001 .

[5]  T. Ledwina,et al.  Data-Driven Rank Tests for Independence , 1999 .

[6]  R. Randles,et al.  A Nonparametric Test of Independence between Two Vectors , 1997 .

[7]  T. Louis,et al.  Tests of independence for bivariate survival data. , 1996, Biometrics.

[8]  Jon A. Wellner,et al.  Weak Convergence and Empirical Processes: With Applications to Statistics , 1996 .

[9]  P. Deheuvels,et al.  Cramer-von mises-type tests with applications to tests of independence for multivariate extreme-value distributions , 1996 .

[10]  Lixing Zhu,et al.  Some blum-kiefer-rosenblatt type tests for the joint independence of variables , 1996 .

[11]  A. Feuerverger,et al.  A Consistent Test for Bivariate Dependence , 1993 .

[12]  J. Wellner,et al.  Empirical Processes with Applications to Statistics , 2009 .

[13]  C. Genest.  Frank's family of bivariate distributions , 1987 .

[14]  P. Gaenssler,et al.  Seminar on Empirical Processes , 1987 .

[15]  Christian Genest,et al.  Copules archimédiennes et families de lois bidimensionnelles dont les marges sont données , 1986 .

[16]  R. Nelsen.  Properties of a one-parameter family of bivariate distributions with specified marginals , 1986 .

[17]  Derek S. Cotterill,et al.  ON THE LIMITING DISTRIBUTION OF AND CRITICAL VALUES FOR THE HOEFFDING, BLUM, KIEFER, ROSENBLATT INDEPENDENCE CRITERION , 1985 .

[18]  Paul Deheuvels,et al.  An asymptotic decomposition for multivariate distribution-free tests of independence , 1981 .

[19]  Miklos Csorgo,et al.  On the limiting distribution of and critical values for the multivariate Cramér-von Mises , 1982 .

[20]  M. Csörgo.  Strong approximations of the Hoeffding, Blum, Kiefer, Rosenblatt multivariate empirical process , 1979 .

[21]  Mir M. Ali,et al.  A class of bivariate distri-butions including the bivariate logistic , 1978 .

[22]  D. Clayton.  A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence , 1978 .

[23]  M. J. Frank.  On the simultaneous associativity of F(x, y) and x+y-F(x, y). (Short Communication). , 1978 .

[24]  Ramon C. Littell,et al.  Asymptotic Optimality of Fisher's Method of Combining Independent Tests , 1971 .

[25]  J. Kiefer,et al.  DISTRIBUTION FREE TESTS OF INDEPENDENCE BASED ON THE SAMPLE DISTRIBUTION FUNCTION , 1961 .

[26]  J. Gil-Pelaez.  Note on the inversion theorem , 1951 .