Box-type approximations in nonparametric factorial designs

Journal of the American Statistical Association

Volumn 92, Issue 440, 1997, Pages 1494-1502

  Brunner, Edgar ^a   Dette, Holger ^b   Munk, Axel ^b  

^a UNIVERSITY OF GÖTTINGEN   (Germany)

^b RUHR UNIVERSITY BOCHUM   (Germany)

Author keywords

Chi squared approximation; Heteroscedastic errors; Nonparametric factorial designs; Quadratic forms; Robust analysis of variance

Indexed keywords

EID: 0031315609     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.1997.10473671     Document Type: Article

References (25)

1. Akritas, M. G.(1990), "The Rank TransformMethod in Some Two-Factor Designs,"Journal of the American Statistical Association, 85, 73-78.
2. Akritas, M. G., and Arnold, S. F.(1994), "Fully NonparametricHypotheses for Factorial Designs I: Multivariate Repeated-Measures Designs,"Journal of the American Statistical Association, 89, 336-343.
3. Akritas, M. G., Arnold, S. F., and Brunner, E.(1997), "NonparametricHypothesesand Rank Statistics for UnbalancedFactorial Designs,"Journal of the American Statistical Association, 92, 258-265.
4. Bishop, T. A., and Dudewicz, E. J.(1978), "Exact Analysis of Variance With Unequal Variances: Test Procedures and Tables,"Technometrics20,419-24.
5. Box, G. E. P.(1954), "Some Theorems on Quadratic Forms Applied in the Study of Analysis of Variance Problems, J. Effect of Inequality of Variance in the One-way Classification," The Annals of Mathematical Statistics, 25, 290-302.
6. Brown, M. B., and Forsythe, A. B.(1974), "The Small Sample Behaviour of Some Statistics Which Test the Equality of Several Means,"Technometrics,16, 129-132.
7. Conerly, M. C; and Mansfield, E. R.(1988), "An Approximate Test for Comparing HeteroscedasticRegression Models,"Journal of the American Statistical Association, 83,811-817.
8. Conover, W.J., and Iman, R.L. (1976), "On Some AlternativeProcedures using Ranks for the Analysis of Experimental Designs," Communications in Statistics, Part A-Theory and Methods 5, 1349-1368.
9. Conover, W.J., and Iman, R.L. (1981), "Rank Transformations as a Bridge Between Parametric and Nonparametric Statistics (with discussion),"The American Statistician,35, 124-133.
10. Hora, S. C. and Conover, W. J.(1984), "The F-Statistic in the Two-Way Layout With Rank Score Transformed Data,"Journal of the American Statistical Association, 79, 668-673.
11. Johnson, N. J., and Kotz, S.(1970), Continuous Univariate Distributions-2. Boston: Houghton Mifflin.
12. Kachar, R. N., and Harville, D. A.(1984), "Approximations for Standard Errors of Estimators for Fixed and Random Effects in Linear Models,"Journal of the American Statistical Association, 79, 853-62.
13. Krutchkoff, R. G.(1988), "One-way Fixed Effects Analysis of Variance When the Error Variances May Be Unequal,"Journal of Statistical Computation and Simulation, 30,259-271.
14. Krutchkoff, R. G. (1989), "Two-way Fixed Effects Analysis of Variance When the Error Variances May Be Unequal,"Journal of Statistical Computation and Simulation, 32, 177-183.
15. Mathai, A. M., and Provost, S. B.(1992), Quadratic Forms in Random Variables, Theory and Applications, New York: Marcel Dekker.
16. Moser, B. K., and Stevens, G. R.(1992), "Homogeneity of Variance in the Two Sample Mean Test,"The American Statistician, 46, 19-21.
17. Patnaik, P. B.(1949), "The Noncentral X2 and F-distributions and Their Applications," Biometrika, 36, 202-232.
18. Roth, A. J.(1983), "Robust Trend Tests Derived and Simulated: Analogs of the Welch and Brown Forsythe Tests,"Journal of the American Statistical Association, 78, 972-980.
19. Rothenberg, T. J.(1984), "Hypothesis Testing in Linear Models When the Error Covariance Matrix Is Nonscalar,"Econometrica, 52, 827-842.
20. Rustagi, J. S.(1976), Variational Methods in Statistics, New York: Academic Press.
21. Thompson, G. L.(1991), "A Unified Approach to Rank Tests for Multivariate and Repeated Measures Designs,"Journal of the American Statistical Association, 86,410-419.
22. Weerahandi, S.(1995a), Exact Statistical Methods for Data Analysis, New York: Springer-Verlag.
23. Weerahandi, S. (1995b), "ANOVA under Unequal Error Variances,"Biometrics, 51, 589-599.
24. Welch, B. L.(1951), "On the Comparison of Several Mean Values,"Biometrika, 38, 330-336.
25. Witting, H., and Müller-Funk, U.(1995), Mathematische Statistik II, Stuttgart: B. G. Teubner.