A path length inequality for the multivariate-t distribution, with applications to multiple comparisons

Journal of the American Statistical Association

Volumn 91, Issue 433, 1996, Pages 211-216

  McCann, Melinda ^a   Edwards, Don ^b  

^a OKLAHOMA STATE UNIVERSITY   (United States)

^b UNIVERSITY OF SOUTH CAROLINA   (United States)

Author keywords

Confidence intervals; Family wise error; Naiman's inequality; Simultaneous inference

Indexed keywords

EID: 0039812879     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.1996.10476678     Document Type: Article

References (24)

1. Bofinger, E. (1985), “Multiple Comparisons and Type III Errors,” Journal of the American Statistical Association, 80, 433-437.
2. Dunnett, C. W. (1964), “New Tables for Multiple Comparisons With a Control,” Biometrics, 20, 482-491.
3. Dunnett, C. W., and Sobel, M. (1954), “A Bivariate Generalization of Student's t Distribution, With Tables for Certain Special Cases,” Biometrika, 31, 153-169.
4. Edwards, D., and Berry, J. J. (1987), “The Efficiency of Simulation-Based Multiple Comparisons,” Biometrics, 43, 913-928.
5. Foutz, R. V. (1981), “Simultaneous Tests for Finite Families of Hypotheses,” Communications in Statistics, Series A-Theory and Methods, 11, 1839-1853.
6. Hahn, G. J., and Hendrickson, R. W. (1971), “A Table of Percentage Points of the Distribution of the Largest Absolute Value of k Student Variates and Its Applications,” Biometrika, 58, 323-332.
7. Hayter, A. J. (1990), “A One-Sided Studentized Range Test for Testing Against a Simple Ordered Alternative,” Journal of the American Statistical Association, 85, 778-785.
8. Hsu, J. C. (1984), “Constrained Two-Sided Simultaneous Confidence Intervals for Multiple Comparisons With the Best,” The Annals of Statistics, 12, 1136-1144.
9. Hunter, D. (1976), “An Upper Bound for the Probability of a Union,” Journal of Applied Probability, 13, 597-603.
10. International Mathematical and Statistical Libraries, Inc. (1987), IMSL User's Manual: Math/Library. Fortran Subroutines for Mathematical Applications, Houston: Author.
11. International Mathematical and Statistical Libraries, Inc. (1987), IMSL User's Manual. Stat/Library. Fortran Subroutines for Statistical Applications, Houston: Author.
12. Kruskal, J. B. (1956), “On the Shortest Spanning Subtree of a Graph and the Traveling Salesman Problem,” Proceedings of the American Mathematical Society, 7, 48-50.
13. Marcus, R. (1978), “Further Results on Simultaneous Confidence Bounds in Normal Models With Restricted Alternatives,” Communications in Statistics, Part A-Theory and Methods, A7, 573-590.
14. Marcus, R. (1982), “Some Results on Simultaneous Confidence Intervals for Monotone Contrasts in One-Way ANOVA Model,” Communications in Statistics, Part A--Theory and Methods, 11, 615-622.
15. Marcus, R., and Peritz, E. (1976), “Some Simultaneous Confidence Bounds in Normal Model With Restricted Alternatives,” Journal of the Royal Statistical Society, Ser. B, 38, 157-165.
16. Naiman, D. Q. (1986), “Conservative Confidence Bands in Curvilinear Regression,” The Annals of Statistics, 14, 896-906.
17. Naiman, D. Q., and Wynn, H. P. (1992), “Inclusion-Exclusion Bonferroni Identities and Inequalities for Discrete Tube-Like Problems via Euler Characteristics,” The Annals of Statistics, 20, 43-76.
18. Scheffe, H. (1953), “A Method for Judging All Contrasts in the Analysis of Variance,” Biometrika, 40, 87-104.
19. Schervish, M. J. (1984), “Multivariate Normal Probabilities With Error Bound, Algorithm AS 195,” Journal of the Royal Statistical Society, Applied Statistics, 33, 81-94.
20. Sidak, Z. (1967), “Rectangular Confidence Regions for the Means of Multivariate Normal Distributions,” Journal of the American Statistical As-sociation, 62, 626-633.
21. Townsend, M. (1987), Discrete Mathematics. Applied Combinatorics and Graph Theory, Menlo Park, CA: Benjamin/Cummings.
22. Uusipaikka, E. (1984), “Exact Confidence Bands on Certain Restricted Sets in the General Linear Model,” unpublished manuscript.
23. Wang, M., and Kennedy, W. J. (1992), “A Numerical Method for Accurately Approximating Multivariate Normal Probabilities,” Computational Statistics and Data Analysis, 13, 197-210.
24. Worsley, K. J. (1982), “An Improved Bonferroni Inequality and Applications,” Biometrika, 69, 297-302.