Locally most powerful rank tests of independence for copula models

References

• Frees , E. W. and Valdez , E. A. 1998 . Understanding relationships using copulas . North American Actuarial Journal , 2 : 1 – 25 .
   Google Scholar
• Embrechts , P. , McNeil , A. J. and Straumann , D. 2002 . “ Correlation and dependence in risk management: properties and pitfalls ” . In Risk Management: Value at Risk and Beyond , United Kingdom: Edited by: Dempster , M. A.H. 176 – 223 . Cambridge : Cambridge University Press .
   Google Scholar
• Mosler , K. and Scarsini , M. 1993 . Stochastic Orders and Applications: A Classified Bibliography , New York : Springer .
   Google Scholar
• Joe , H. 1997 . Multivariate Models and Dependence Concepts , London : Chapman and Hall .
   Google Scholar
• Nelsen , R. B. 1999 . An Introduction to Copulas, Lecture Notes in Statistics No. 139 , New York : Springer .
   Google Scholar
• Drouet-Mari , D. and Kotz , S. 2001 . Correlation and Dependence , London : Imperial College Press .
   Google Scholar
• Bhuchongkul , S. 1964 . A class of nonparametric tests for independence in bivariate populations . The Annals of Mathematical Statistics , 35 : 138 – 149 .
   Google Scholar
• Behnen , K. 1971 . Asymptotic optimality and ARE of certain rank-order tests under contiguity . The Annals of Mathematical Statistics , 42 : 325 – 329 .
   Google Scholar
• Behnen , K. 1972 . A characterization of certain rank-order tests with bounds for the asymptotic relative efficiency . The Annals of Mathematical Statistics , 43 : 1839 – 1851 .
   Google Scholar
• Shirahata , S. 1974 . Locally most powerful rank tests for independence . Bulletin of Mathematical Statistics , 16, 11–21
   Google Scholar
• Shirahata , S. 1975 . Locally most powerful rank tests for independence with censored data . The Annals of Statistics , 3 : 241 – 245 .
   Google Scholar
• Ciesielska , L. and Ledwina , T. 1983 . On locally most powerful rank tests of independence . Zastosowania Matematyki , 18 : 61 – 66 .
   Google Scholar
• Stuart , A. 1954 . The asymptotic relative efficiencies of tests and the derivatives of their power functions . Skandinavisk Aktuarietidskrift , 37 : 163 – 169 .
   Google Scholar
• Konijn , H. S. 1956 . On the power of certain tests of independence in bivariate populations . The Annals of Mathematical Statistics , 27 : 300 – 323 .
   Google Scholar
• Gokhale , D. V. 1968 . On asymptotic relative efficiencies of a class of rank tests for independence of two variables . Annals of the Institute of Statistical Mathematics , 20 : 255 – 261 .
   Google Scholar
• Hájek , J. and [Sbreve]idák , Z. 1967 . Theory of Rank Tests , New York : Academic Press .
   Google Scholar
• Garralda-Guillem , A. I. 1997 . Dependencia y tests de rangos para leyes bidimensionales , Granada, , Spain : Unpublished doctoral dissertation, Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada .
   Google Scholar
• Plackett , R. L. 1965 . A class of bivariate distributions . Journal of the American Statistical Association , 60 : 516 – 522 .
   Web of Science ®Google Scholar
• Ali , M. M. , Mikhail , N. N. and Haq , M. S. 1978 . A class of bivariate distributions including the bivariate logistic . Journal of Multivariate Analysis , 8 : 405 – 412 .
   Web of Science ®Google Scholar
• Frank , M. J. 1979 . On the simultaneous associativity of F(x, y) and . Aequationes Mathe-maticae , 19 : 194 – 226 .
   Google Scholar
• Oakes , D. and Wang , A. 2003 . Copula model generated by Dabrowska’s association measure . Biometrika , 90 : 478 – 481 .
   Google Scholar
• Genest , C. and MacKay , R. J. 1986 . Copules archimédiennes et familles de lois bidimensionnelles dont les marges sont données . The Canadian Journal of Statistics , 14 : 145 – 159 .
   Web of Science ®Google Scholar
• Puri , M. L. and Sen , P. K. 1971 . Nonparametric Methods in Multivariate Analysis , New York : Wiley .
   Google Scholar
• Clayton , D. G. 1978 . “ A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence ” . In Biometrika Vol. 65 , 141 – 151 .
   Google Scholar
• David , H. A. 1982 . Order Statistics , (2nd edn) , New York : Wiley .
   Google Scholar
• Gumbel , E. J. 1960 . Bivariate exponential distributions . Journal of the American Statistical Association , 55 : 698 – 707 .
   Web of Science ®Google Scholar
• Barnett , V. 1980 . Some bivariate uniform distributions . Communications in Statistics, Theory and Methods , 9 : 453 – 461 .
   Web of Science ®Google Scholar
• Verret , F. , 2003, Tests de rangs localement les plus puissants pour l’hypothèse d’indépendance bivariée . Unpublished Master’s thesis No 21063 , Université Laval , Québec , Canada .
   Google Scholar
• van der Vaart , A. W. 1998 . Asymptotic Statistics , Cambridge, , United Kingdom : Cambridge University Press .
   Google Scholar
• van Eeden , C. 1963 . The relation between Pitman’s asymptotic relative efficiency of two tests and the correlation coefficient between their test statistics . The Annals of Mathematical Statistics , 34 : 1442 – 1451 .
   Google Scholar
• Genest , C. , Ghoudi , K. and Rivest , L.-P. 1995 . A semiparametric estimation procedure of dependence parameters in multivariate families of distributions . Biometrika , 82 : 543 – 552 .
   Web of Science ®Google Scholar
• Blest , D. C. 2000 . Rank correlation—An alternative measure . Australian and New Zealand Journal of Statistics , 42 : 101 – 111 .
   Google Scholar
• Genest , C. and Plante , J.-F. 2003 . On Blest’s measure of rank correlation . The Canadian Journal of Statistics , 31 : 35 – 52 .
   Web of Science ®Google Scholar
• Cooke , R. M. and Waij , R. 1986 . Monte Carlo sampling for generalized knowledge dependence with application to human reliability . Risk Analysis , 6 : 335 – 343 .
   PubMed Web of Science ®Google Scholar
• Ferguson , T. S. 1995 . A class of bivariate uniform distributions . Statistical Papers , 36 : 41 – 30 .
   Google Scholar
• Gieser , P. W. and Randles , R. H. 1997 . A nonparametric test of independence between two vectors . Journal of the American Statistical Association , 92 : 561 – 567 .
   Web of Science ®Google Scholar
• Cuzick , J. 1982 . Rank tests for association with right censored data . Biometrika , 69 : 351 – 364 .
   Web of Science ®Google Scholar
• Shih , J. H. and Louis , T. A. 1996 . Tests of independence for bivariate survival data . Biometrics , 52 : 1440 – 1449 .
   PubMedGoogle Scholar
• Säid , M. , Ghazzali , N. and Rivest , L.-P. 2003 . “ Score tests for dependent censoring with survival data ” . In Mathematical Statistics and Applications: Festschrift for Constance van Eeden, IMS Lecture Notes, Monograph Series , CA: Edited by: Moore , M. , Froda , S. and Léger , C. Vol. 42 , 435 – 461 . Hayward : Institute of Mathematical Statistics .
   Google Scholar
• Kallenberg , W. C.M. and Ledwina , T. 1999 . Data-driven rank tests for independence . Journal of the American Statistical Association , 94 : 285 – 301 .
   Web of Science ®Google Scholar
• Hallin , M. and Puri , M. L. 1992 . “ Rank tests for time series analysis: a survey ” . In New Directions in Time Series Analysis , Edited by: Brillinger , D. R. , Parzen , E. and Rosenblatt , M. 112 – 153 . New York : Springer .
   Google Scholar
• Hoeffding , W. 1948 . A non-parametric test of independence . The Annals of Mathematical Statistics , 19 : 546 – 557 .
   Google Scholar
• Blum , J. R. , Kiefer , J. and Rosenblatt , M. 1961 . Distribution free tests of independence based on the sample distribution function . The Annals of Mathematical Statistics , 32 : 485 – 498 .
   Google Scholar
• Genest , C. and Rémillard , B. 2004 . Tests of independence and randomness based on the empirical copula process . Test , 13 : 335 – 369 .
   Web of Science ®Google Scholar