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Simultaneous inferences: new method of maximum combination

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  • A. Martín Andrés
  • M. Álvarez Hernández

Abstract

The Scheffé method is used to carry out simultaneous inferences on many linear combinations of $$K$$ K parameters. Frequently these combinations arise from the need to explain the causes of significance of the homogeneity test for all the parameters. This paper proposes an alternative methodology based on the maximization of the contrast statistic in the coefficient of the combination. This new method, compatible with Scheffé’s method, in addition yields the statistic which should be used for the global test, as well as the combination of maximum significance. The method is illustrated in the cases of $$K$$ K means of normal distributions and $$K$$ K binomial proportions (independent samples). In the second case, the method allows a homogeneity test that is more powerful than Pearson’s classic chi-squared test to be obtained. The program which determines this may be obtained at http://www.ugr.es/local/bioest/Z_LINEAR_K.EXE . Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • A. Martín Andrés & M. Álvarez Hernández, 2015. "Simultaneous inferences: new method of maximum combination," Statistical Papers, Springer, vol. 56(4), pages 1099-1113, November.
    • Handle: RePEc:spr:stpapr:v:56:y:2015:i:4:p:1099-1113
    DOI: 10.1007/s00362-014-0627-1
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    References listed on IDEAS

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    1. Zou, Guang Yong & Huang, Wenyi & Zhang, Xiaohe, 2009. "A note on confidence interval estimation for a linear function of binomial proportions," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1080-1085, February.
    2. Price, Robert M. & Bonett, Douglas G., 2004. "An improved confidence interval for a linear function of binomial proportions," Computational Statistics & Data Analysis, Elsevier, vol. 45(3), pages 449-456, April.
    3. Zhongxue Chen & Hon Ng & Saralees Nadarajah, 2014. "A note on Cochran test for homogeneity in one-way ANOVA and meta-analysis," Statistical Papers, Springer, vol. 55(2), pages 301-310, May.
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