On the multivariate runs test

Annals of Statistics

Volumn 27, Issue 1, 1999, Pages 290-298

  Henze, Norbert ^a   Penrose, Mathew D ^b  

^a UNIVERSITY OF KARLSRUHE   (Germany)

^b DURHAM UNIVERSITY   (United Kingdom)

Author keywords

Homogeneous Poisson process; Minimal spanning tree; Multivariate runs test; Multivariate two sample problem

Indexed keywords

EID: 0033243864     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1018031112     Document Type: Article

References (22)

1. ALDOUS, D. (1990). A Random tree model associated with random graphs. Random Structures Algorithms 1 383-401.
2. ALDOUS, D. and STEELE, J. M. (1992). Asymptotics for Euclidean minimal spanning trees on random points. Probab. Theory Related Fields 92 247-258.
3. ANDERSON, N. H., HALL, P. and TITTERINGTON, D. M. (1994). Two-sample test statistics for measuring discrepancies between two multivariate probability density functions using kernel-based density estimates. J. Multivariate Anal. 50 41-54.
4. BAHR, R. (1996). A new test for the multivariate two-sample problem with general alternatives (in German). Doctoral thesis, Univ. Hannover.
5. BLOEMENA, A. R. (1964). Sampling from a graph. Mathematical Centre Tracts 2. Math. Centrum, Amsterdam.
6. m and measure-valued martingales. Report S98-2, Dept. Statistics, Univ. New South Wales, Sidney.
7. FERGER, D. (1997). Optimal tests for the general two-sample problem. Dresdener Schriften zur Mathematischen Stochastik Technische Univ. Dresden.
8. FRIEDMAN, J. H. and RAFSKY, L. C. (1979). Multivariate generalizations of the Wolfowitz and Smirnov two-sample tests. Ann. Statist. 7 697-717.
9. GYÖRFI, L. and NEMETZ, T. (1975). f-dissimilarity: A general class of separation measures of several probability measures. In Topics in Information Theory. Colloq. Math. Soc. János Bolyai 16 309-321.
10. GYÖRFI, L. and NEMETZ, T. (1977). On the dissimilarity of probability measures. Problems Control Inform. Theory 6 263-267.
11. GYÖRFI, L. and NEMETZ, T. (1978). f-dissimilarity. A generalization of affinity of several distributions. Ann. Inst. Statist. Math. 30 105-113.
12. HENZE, N. (1986). On the probability that a random point is the jth nearest neighbour to its own kth nearest neighbour. J. Appl. Probab. 23 221-226.
13. HENZE, N. (1988). A multivariate two-sample test based on the number of nearest-neighbor type coincidences. Ann. Statist. 16 772-783.
14. HENZE, N. and VOIGT, B. (1992). Almost sure convergence of certain slowly changing symmetric one- and multi-sample statistics. Ann. Probab. 20 1086-1098.
15. KINGMAN, J. F. C. (1993). Poisson Processes, Oxford Univ. Press.
16. LEE, S. (1997). The central limit theorem for Euclidean minimal spanning trees I. Ann. Appl. Probab. 7 996-1020.
17. PENROSE, M. D. (1996). The random minimal spanning tree in high dimensions. Ann. Probab. 24 1903-1925.
18. PICKARD, D. K. (1982). Isolated nearest neighbours. J. Appl. Probab. 19 444-449.
19. RESNICK, S. I. (1987). Extreme Values, Regular Variation, and Point Processes. Springer, New York.
20. RUDIN, W. (1987). Real and Complex Analysis, 3rd ed. McGraw-Hill, New York.
21. SCHILLING, M. F. (1986). Multivariate two-sample tests based on nearest neighbors. J. Amer. Statist. Assoc. 81 799-806.
22. STEELE, J. M., SHEPP, L. A. and EDDY, W. F. (1987). On the number of leaves of a Euclidean minimal spanning tree. J. Appl. Prob. 24 809-826.