On the two-sample behrens-fisher problem for functional data

Journal of Statistical Theory and Practice

Volumn 4, Issue 4, 2010, Pages 571-587

  Zhang, Jin Ting ^a   Liang, Xuehua ^a   Xiao, Shengning ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

(formula presented) consistency; Behrens Fisher problem; L2 norm based test; Two sample test; Welch type method; 2 approximation; 2 type mixture

Indexed keywords

EID: 84994852716     PISSN: 15598608     EISSN: 15598616     Source Type: Journal    
DOI: 10.1080/15598608.2010.10412005     Document Type: Article

References (39)

1. Algina, J., Tang, K., 1988. Type I error rates for Yao’s and James’s tests of equality of mean vectors under variance-covariance heteroscedasticity. J. Educ. Statist., 13, 281–290.
2. Behrens, B.V., 1929. Ein Beitrag zur Fehlerberechnung bei wenige Beobachtungen. Landwirtschaftliches Jahresbuch, 68, 807–837.
3. Bennett, B.M., 1951. Note on a solution of the generalized Behrens-Fisher problem. Ann. Inst. Statist. Math., 2, 87–90.
4. Buckley, M.J., Eagleson, G.K., 1988. An approximation to the distribution of quadratic forms in normal random variables. Austral. J. Statist., 30A, 150–159.
5. Cuevasa, A., Febrerob, M., Fraimanc, R., 2004. An anova test for functional data. Comput. Statist. and Data Anal., 47, 111–122.
6. Dong, L., 2004. The Behrens-Fisher problem: an empirical likelihood approach. Technical report, Marcel Dekker, New York.
7. Eubank, R.L., 1999. Nonparametric Regression and Spline Smoothing. Marcel Dekker, New York.
8. Fan, J., Gijbels, I., 1996. Local Polynomial Modeling and its Applications. Chapman and Hall, London.
9. Faraway, J.J., 1997. Regression analysis for a functional response. Technometrics, 39, 254–261.
10. Fisher, R.A., 1935. The fiducial argument in statistical inference. Ann. Eugenics., 11, 141–172.
11. Ghosh, M., Kim, Y.H., 2001. The Behrens-Fisher problem revisited: A Bayes-frequentist synthesis. Canadian J. of Statist., 29, 1–14.
12. Green, P.J., Silverman, B.W., 1994. Nonparametric Regression and Generalized Linear Models. Chapman and Hall, London.
13. Hall, P., van Keilegom, I., 2007. Two-sample tests in functional data analysis starting from discrete data. Statist. Sinica., 17, 1511–1531.
14. James, G.S., 1954. Tests of linear hypotheses in univariate and multivariate analysis when the ratios of the population variances are unknown. Biometrika, 41, 19–43.
15. Johansen, S., 1980. The Welch-James approximation to the distribution of the residual sum of squares in a weighted linear regression. Biometrika, 67, 85–95.
16. Kim, S-J., 1992. Practical solution to the multivariate Behrens-Fisher problem. Biometrika, 79, 171–176.
17. Krishnamoorthy, K., Lu, F., 2009. A parametric bootstrap solution to the MANOVA under heteroscedastic- ity. J. Statist. Comput. and Simul., to appear.
18. Krishnamoorthy, K., Lu, F., Mathew, T., 2007. A parametric bootstrap approach for ANOVA with unequal variances: fixed and random models. Comput. Stat. Data Anal., 51, 5731–5742.
19. Krishnamoorthy, K., Xia, Y., 2006. On selecting tests for equality of two normal mean vectors. Multi. Behavioral Res., 41, 533–548.
20. Krishnamoorthy, K., Yu, J., 2004. Modified Nel and Van der Merwe test for the multivariate Behrens-Fisher problem. Statist. and Prob. letters., 66, 161–169.
21. Lee, A., Gurland, J., 1975. Size and power of tests for equality of means of two normal populations with unequal variances. J. Amer. Statist. Assoc., 70, 933–947.
22. Mas, A., 2007. Testing for the mean of random curves: a penalization approach. Statist. Infer. Stoch. Proc., 10, 147–163.
23. Nel, D.G., Van der Merwe, 1986. A solution to the multivariate Behrens-Fisher problem. Comm. Statist.- Theory Methods, 15, 3719–3735.
24. Ramsay, J.O., Silverman, B.W., 2002. Applied Functional Data Analysis: Methods and Case Studies. Springer-Verlag, New York.
25. Ramsay, J.O., Silverman, B.W., 2005. Functional Data Analysis, 2nd edition. Springer-Verlag, New York.
26. Ruppert, D., Wand, M.P., Carroll. R.J., 2003. Semiparametric Regression. Cambridge University Press, London.
27. Scheffe, H., 1970. Practical solutions of the Behrens-Fisher problem. J. Amer. Statist. Assoc., 65, 1501–1508.
28. Shen, Q., Faraway, J.J., 2004. An F test for linear models with functional responses. Statist. Sinica, 14, 1239–1257.
29. Tang, S., Tsui, K.W., 2005. Distributional properties for the generalized P-value for the Behrens-Fisher problem. Statist. and Prob. letters, 77,1–8.
30. Tuddenham, R.D., Snyder, M.M., 1954. Physical growth of California boys and girls from birth to eighteen years. Univ. Calif. Publ. Chld. Devlpmnt., 1,183–364.
31. Wahba, G., 1990. Spline models for observational data. CBMS-NSF Regional Conference Series in Applied Mathematics - 59, SIAM, Philadelphia.
32. Wand, M.P., Jones, M.C., 1995. Kernel Smoothing. Chapman and Hall, London.
33. Weerahandi, S., 1993. Generalized confidence intervals. J. Amer. Statist. Assoc., 88, 899–905.
34. Welch, B.L., 1947. The generalization of Student’s problem when several different population variances are involved. Biometrika, 34, 28–35.
35. Yao, Y., 1965. An approximate degrees of freedom solution to the multivariate Behrens-Fisher problem. Biometrika, 52,139–147.
36. Zhang, J.T., Chen, J.W., 2007. Statistical inference for functional data. Ann. Statist., 35, 1052–1079.
37. 2-type mixtures with application. J. Amer. Statist. Assoc., 100, 273–285.
38. Zhang, J.T., 2010. Statistical inferences for linear models with functional responses. Statist. Sinica, to appear.
39. Zhang, C.Q., Peng, H., Zhang, J.T., 2010. Two-sample tests for functional data. Comm. Statist.- Theory Methods, 39, 559–578.