Abstract
After defining robustness for interval estimations and tests, the paper presents an exact method for investigating this property for discrete distributions with finite supports. This method is used to investigate the u- and t-tests in the case of the single sample problem for robustness in respect of two and three point distributions.
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References
Bickel, P. J. Another look at Robustness: A review of reviews and some new developments. Scand. J. Statist, 3 (1976), 145–168.
Guiard, G. (ed.) Robustheit II. Arbeitsmaterial zum Forschungsthema Robustheit. Probleme der angewandten Statistik (1981) 5.
Herrendörfer, G. (ed.) Robustheit I. Arbeitsmaterial zum Forschungsthema Robustheit. Probleme der angewandten Statistik (1980) 4.
Herrendörfer, G., Rasch, D., Feige, K.-D. Robustness of satistical methods II. Methods for the ons sample problem. Biom. Journ. 25 (1983) 327–343.
Ito, K. Robustness of ANOVA and MANOVA test procedures. Handbook of Statistics, I (P. R. Krishnaiah, Ed.). North-Holland Publishing Company (1980), 199–236.
Mandelbrot, B. The role of sufficiency and of estimation in thermodynamics. Ann. Math. Statist. 33 (1962), 1021–1038.
Posten, H. O. The robustness of the two-sample t-test over the Pearson system. J. Stat. Comp. Simul., 6 (1978), 295–311.
Posten, H. O. The robustness of the one-sample t-test over the Pearson system. J. Statist. Comp. Simul. 9 (1979), 133–149.
Rasch, D. und Herrdörfer, G. (ed.) Robustheit III. Arbeitsmaterial zum Forschungsthema Rebustheit. Probleme der angewandten Statistik (1982) 7.
Rey, W. J. J. Robust statistical methods. Springer Verlag Berlin (1978), Berlin — Heidelberg — NewYork: Springer Verlag 1978.
Rider, P. R. On the distribution of the ratio of mean to standard deviation in small samples from non normal universes. Biometrika 21 (1929), 124–143.
Tan, W. Y. Sampling distributions and robustness of t, F and variance ratio in two samples and ANOVA models with respect to departure from normality. Memphis State University, 1982, 28 Seiten.
Tiku, M. L. Languerre series forms of the distributions of classical test-statistics and their robustness in nonnormal situations. Applied Statistics. (R. P. Gupta, Ed.) American Elsevier Pub., Comp., NewYork, 1975.
Tukey, J. W. Where do we go from here? J. Amer. Statist. Ass. 55 (1960), 80–93.
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© 1984 Academy of Agricultural Sciences of the GDR, Research Centre of Animal Production, Dummerstorf-Rostock, DDR 2551 Dummerstorf.
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Herrendörfer, G., Feige, KD. (1984). A Combinatorial Method in Robustness Research and Two Applications. In: Rasch, D., Tiku, M.L. (eds) Robustness of Statistical Methods and Nonparametric Statistics. Theory and Decision Library, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6528-7_12
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DOI: https://doi.org/10.1007/978-94-009-6528-7_12
Publisher Name: Springer, Dordrecht
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