Rank statistics under dependent observations and applications to factorial designs

Abstract Rank statistics for multivariate designs of independent random vectors of varying dimension are shown to be asymptotically normal, even in case the dimensions tend to infinity. The asymptotic variance is estimated consistently. The result extends those by various other authors and applies to simple linear rank statistics as well as to signed rank statistics which can be handled as a special case of simple linear rank statistics under dependence.

[1]  Edgar Brunner,et al.  RANK TESTS IN 2X2 DESIGNS , 1986 .

[2]  W. Hoeffding.  On the Centering of a Simple Linear Rank Statistic , 1973 .

[3]  Larry P. Ammann,et al.  Efficiencies of Interblock Rank Statistics for Repeated Measures Designs , 1990 .

[4]  G. L. Thompson.  Asymptotic distribution of rank statistics under dependencies with multivariate application , 1990 .

[5]  Herman Chernoff,et al.  ASYMPTOTIC NORMALITY AND EFFICIENCY OF CERTAIN NONPARAMETRIC TEST STATISTICS , 1958 .

[6]  F. Ruymgaart,et al.  Asymptotic normality of multivariate linear rank statistics in the non-I.I.D. case , 1978 .

[7]  Manfred Denker.  Asymptotic Distribution Theory in Nonparametric Statistics , 1985 .

[8]  J. Hájek,et al.  Asymptotic Normality of Simple Linear Rank Statistics Under Alternatives II , 1968 .

[9]  P. Sen,et al.  Nonparametric methods in multivariate analysis , 1974 .

[10]  P. Sen,et al.  Nonparametric Methods in General Linear Models. , 1986 .

[11]  E Brunner,et al.  A nonparametric estimator of the shift effect for repeated observations. , 1991, Biometrics.

[12]  George E. Policello,et al.  Robust Rank Procedures for the Behrens-Fisher Problem , 1981 .

[13]  G. L. Thompson.  A Unified Approach to Rank Tests for Multivariate and Repeated Measures Designs , 1991 .

[14]  Edgar Brunner,et al.  Two — Sample Rank Tests in General Models , 1986 .

[15]  M. Hušková.  Asymptotic distribution of simple linear rank statistics for testing symmetry , 1970 .

[16]  Edgar Brunner,et al.  Rank Tests for correlated Random Variables , 1982 .

[17]  M. Denker,et al.  SOME CONTRIBUTIONS TO CHERNOFF-SAVAGE THEOREMS , 1985 .

[18]  E. Brunner,et al.  Rank tests for the 2×2 split plot design , 1984 .

[19]  M. Denker,et al.  A sharpening of the remainder term in the higher-dimensional central limit theorem for multilinear rank statistics , 1985 .

[20]  Larry P. Ammann,et al.  Efficacies of Rank-Transform Statistics in Two-Way Models with No Interaction , 1989 .

[21]  W. J. Conover,et al.  The F Statistic in the Two-Way Layout With Rank–Score Transformed Data , 1984 .

[22]  R. Pyke,et al.  Weak Convergence of a Two-sample Empirical Process and a New Approach to Chernoff-Savage Theorems , 1968 .

[23]  Holger Dette,et al.  Rank procedures for the two-factor mixed model , 1992 .

[24]  Manfred Denker,et al.  A moment estimate for rank statistics , 1985 .