Testing homogeneity of multivariate normal mean vectors under an order restriction when the covariance matrices are common but unknown

Annals of Statistics

Volumn 31, Issue 5, 2003, Pages 1517-1536

  Sasabuchi, Shoichi ^a   Tanaka, Koji ^b   Tsukamoto, Takeshi ^c  

^a KYUSHU UNIVERSITY   (Japan)

^b Tosu High School   (Japan)

^c HITACHI LTD   (Japan)

Author keywords

Common but unknown covariance matrices; Multivariate isotonic regression; Multivariate normal distribution; Order restriction; Testing homogeneity of mean vectors; Upper tail probability

Indexed keywords

EID: 0242595972     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1065705117     Document Type: Article

References (12)

1. ANDERSON, T. W. (1984). An Introduction to Multivariate Statistical Analysis, 2nd ed. Wiley, New York.
2. BARLOW, R. E., BARTHOLOMEW, D. J., BREMNER, J. M. and BRUNK, H. D. (1972). Statistical Inference under Order Restrictions: The Theory and Application of Isotonic Regression. Wiley, New York.
3. BARTHOLOMEW, D. J. (1959). A test of homogeneity for ordered alternatives. Biometrika 46 36-48.
4. BARTHOLOMEW, D. J. (1961). Ordered tests in the analysis of variance. Biometrika 48 325-332.
5. KULATUNGA, D. D. S. (1984). Convolutions of the probabilities P(l, k) used in order restricted inference. Mem. Fac. Sci. Kyushu Univ. Ser. A Math. 38 9-15.
6. KULATUNGA, D. D. S. and SASABUCHI, S. (1984). A test of homogeneity of mean vectors against multivariate isotonic alternatives. Mem. Fac. Sci. Kyushu Univ. Ser. A Math. 38 151-161.
7. NOMAKUCHI, K. and SHI, N.-Z. (1988). A test for a multiple isotonic regression problem. Biometrika 75 181-184.
8. PERLMAN, M. D. (1969). One-sided testing problems in multivariate analysis. Ann. Math. Statist. 40 549-567.
9. ROBERTSON, T., WRIGHT, F. T. and DYKSTRA, R. L. (1988). Order Restricted Statistical Inference. Wiley, New York.
10. SASABUCHI, S., INUTSUKA, M. and KULATUNGA, D. D. S. (1983). A multivariate version of isotonic regression. Biometrika 70 465-472.
11. SASABUCHI, S., INUTSUKA, M. and KULATUNGA, D. D. S. (1992). An algorithm for computing multivariate isotonic regression. Hiroshima Math. J. 22 551-560.
12. SASABUCHI, S., KULATUNGA, D. D. S. and SAITO, H. (1998). Comparison of powers of some tests for testing homogeneity under order restrictions in multivariate normal means. Amer. J. Math. Management Sci. 18 131-158.