Multiple comparisons for a large number of parameters

Biometrical Journal

Volumn 43, Issue 5, 2001, Pages 627-643

  Sun, Jiayang ^a  

^a CASE WESTERN RESERVE UNIVERSITY   (United States)

Author keywords

Discrete and continuous domains; Gaussian random fields; Generalized linear models; Maximum; Regression; Simultaneous confidence intervals or regions; Tube methods

Indexed keywords

REGRESSION ANALYSIS; UNCERTAINTY ANALYSIS;

CONFIDENCE REGION; CONTINUOUS DOMAIN; DISCRETE DOMAINS; GAUSSIAN RANDOM FIELDS; GENERALIZED LINEAR MODEL; MAXIMUM; REGRESSION; SIMULTANEOUS CONFIDENCE INTERVAL OR REGION; SIMULTANEOUS CONFIDENCE INTERVALS; TUBE METHODS;

GAUSSIAN DISTRIBUTION;

EID: 0035641767     PISSN: 03233847     EISSN: None     Source Type: Journal    
DOI: 10.1002/1521-4036(200109)43:5<627::AID-BIMJ627>3.0.CO;2-F     Document Type: Article

References (37)

1. ADLER, R., J., 1981: The geometry of random fields. Wiley Series in Probability and Mathematical Statistics. John Wiley & Sons, Ltd.
2. ADLER, R., J., 2000: On excursion sets, tube formulas and maxima of random fields. Ann. Appl. Probab. 10, no. 1, 1-74.
3. ALDOUS, D., 1989: Probability approximations via the Poisson clumping heuristic. Applied Mathematical Sciences 77. Springer-Verlag, New York-Berlin.
4. BICKEL, P. and ROSENBLATT, M., 1973: Two dimensional random fields. In: Multivariate Analysis-III, P. K. Krishnaiah, ed.. Academic Press, New York, 3-15.
5. FARAWAY, J. J. and SUN, J.,1995: Simultaneous Confidence Bands for Linear Regression with Heteroscedastic Errors. J. Amer. Statist. Assoc. 90, No 431, 1094-1098.
6. ELSTON, R. C. and GRIZZLE, J. E., 1962: Estimation of time-response curves and their confidence bounds. Biometrics 18, 148-159.
7. HOGAN, M. L. and SIEGMUND, D., 1986: Large Deviations for the Maxima of Some Random Fields. Adv. Appl. Mathematics 7, 2-22.
8. HOTELLING, H., 1939: Tubes and Spheres in n-space, a Class of Statistical Problems. American J. Math. 61, 440-460.
9. HSU, J. C., 1996: Multiple comparisons. Theory and methods. Chapman & Hall, London.
10. HALL, P. and TITTERINGTON, D. M., 1988: On confidence bands in nonparametric density estimation and regression. J. Multivariate Anal. 27, 228-254.
11. HÄRDLE, W. and MARRON, J. S., 1991: Bootstrap simultaneous error bars for nonparametric regression. Ann. Statist. 19, 778-796.
12. HOCHBERG, Y. and YAMHANE, A. C., 1987: Multiple comparison Procedures. Wiley, New York.
13. JOHANSEN, S. and JOHNSTONE, I., 1990: Hotelling's Theorem on the volume of tubes: some illustrations in simultaneous inference and data analysis. Ann. Statist. 18, 652-684.
14. KNAFL, G.; SACKS, J., and YLVISAKER, D., 1985: Confidence Bands for Regression Functions. J. Amer. Statist. Assoc. 80, 683-691.
15. KNOWLES, M. and SIEGMUND, D., 1989: On Hotelling's Geometric Approach to Testing for a Nonlinear Parameter in Regression. Internat. Statist. Rev. 57, 205-220.
16. KOCH, H.-F. and HOTHORN, L. A., 1999: Exact unconditional distributions for dichotomous data in many-to-one comparisons. J. Statist. Plann. Inference 82, no. 1-2, 83-99.
17. KREYSZIG, E., 1968: Introduction to Differential Geometry and Riemannian Geometry. University of Toronto Press.
18. LOADER, C., 1993: Nonparametric regression, confidence bands and bias correction. Proceedings of the 25th Symposium on the Interface Between Computer Science and Statistics, 131-136.
19. LOADER, C. R., 1999: Local Likelihood and Regression. Springer. (See http://cm.bell-labs.com/stat/project/locfit/ to download source code Locfit.)
20. LOADER, C. R. and SUN, J., 1997: Robustness of Tube Formula. J. Comp. Graph. Statist. 6, No 2, pp. 242-50.
21. MCCANN, M. and EDWARDS, D., 1996: A path length inequality for the multivariate-t distribution, with applications to multiple comparisons. J. Amer. Statist. Assoc. 91, no. 433, 211-216.
22. MCP 2000, the 2nd International Conference on Multiple Comparisons with medical applications, organized by Ludwig Hothorn (http://www.bioinf.uni-hannover.de/̃mcp2000/:
23. NAIMAN, D. Q., 1986: Conservative Confidence Bands in Curvilinear Regression. Ann. Statist. 14, 896-906.
24. NAIMAN, D. Q. and WYNN, H. P., 1997: Abstract tubes, improved inclusion-exclusion identities and inequalities and importance sampling. Ann. Statist. 25, no. 5, 1954-1983.
25. RICE, S. O., 1939: The distribution of the maxima of a random curve. Amer. J. Math. 61, 409-416.
26. SCHEFFE, H., 1959: The Analysis of Variance. John Wiley & Sons, New York.
27. SPURRIER, J. D., 1999: Exact confidence bounds for all contrasts of three or more regression lines. J. Amer. Statist. Assoc. 94, no. 446, 483-488.
28. SUN, J., 1991: Significance Levels in Exploratory Projection Pursuit. Biometrika 78, pp. 759-769.
29. SUN, J., 1993: Tail Probabilities of the Maxima of Gaussian Random Fields. Annals of Probability: 21, 34-71.
30. SUN, J. and LOADER, C. R., 1994: Simultaneous Confidence Bands for Linear Regression and Smoothing. Ann. Statist. 22, No. 3, pp. 1328-1346.
31. SUN, J., RAZ, J., and FARAWAY, J. J., 1999: Simultaneous Confidence Bands for Growth and Response Curves. Statistica Sinica. Vol. 9, No. 3, pp. 679-698.
32. SUN, J., LOADER, C. R., and MCCORMICK, W. P., 2000: Confidence Bands in Generalized Linear Models. Ann. Statist. 28, NO. 2, 429-460.
33. UUSIPAIKKA, E., 1983: Exact Confidence Bands for Linear Regression over Intervals. J. Amer. Statist. Assoc. 78, 638-644.
34. WEYL, H., 1939: On the Volume of Tubes. Amer. J. Math. 61, 461-472.
35. 2, F and t fields. Adv. in Appl. Probab. 26, 13-41.
36. WORSLEY, K. J., 1996: The geometry of random images. CHANCE 9 1: 27-40.
37. WYNN, H. P., 1984: An Exact Confidence Band for One-Dimensional Polynomial Regression. Biometrika 71, 375-380.