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Simultaneous testing for the successive differences of exponential location parameters under heteroscedasticity

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  • Maurya, Vishal
  • Goyal, Anju
  • Gill, Amar Nath

Abstract

In this paper, the design-oriented two-stage and data-analysis one-stage multiple comparison procedures for successive comparisons of exponential location parameters under heteroscedasticity are proposed. One-sided and two-sided simultaneous confidence intervals are also given. We also extend these simultaneous confidence intervals for successive differences to a larger class of contrasts of the location parameters. Upper limits of critical values are obtained using the recent techniques given in Lam [Lam, K., 1987. Subset selection of normal populations under heteroscedasticity. In: Proceedings of the Second International Advanced Seminar/Workshop on Inference Procedures Associated with Statistical Ranking and Selection, Sydney, Australia; Lam, K., 1988. An improved two-stage selection procedure. Communications in Statistics Simulation and Computation. 17 (3), 995-1006]. These approximate critical values are shown to have better results than the approximate critical values using the Bonferroni inequality developed in this paper. Finally, the application of the proposed procedures is illustrated with an example.

Suggested Citation

  • Maurya, Vishal & Goyal, Anju & Gill, Amar Nath, 2011. "Simultaneous testing for the successive differences of exponential location parameters under heteroscedasticity," Statistics & Probability Letters, Elsevier, vol. 81(10), pages 1507-1517, October.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:10:p:1507-1517
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    References listed on IDEAS

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    1. N. J. Hill & A. R. Padmanabhan & Madan L. Puri, 1988. "Adaptive Nonparametric Procedures and Applications," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 37(2), pages 205-218, June.
    2. Hayter, A. J. & Liu, W., 1996. "Exact calculations for the one-sided studentized range test for testing against a simple ordered alternative," Computational Statistics & Data Analysis, Elsevier, vol. 22(1), pages 17-25, June.
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    Cited by:

    1. Anjana Mondal & Markus Pauly & Somesh Kumar, 2024. "Testing against ordered alternatives in one-way ANOVA model with exponential errors," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(4), pages 649-678, August.
    2. Mahmood Kharrati-Kopaei & Ahad Malekzadeh, 2019. "On the exact distribution of the likelihood ratio test for testing the homogeneity of scale parameters of several two-parameter exponential distributions: complete and censored samples," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(4), pages 409-427, May.
    3. Shu-Fei Wu, 2020. "One-Stage Multiple Comparisons with the Control for Exponential Median Lifetimes under Heteroscedasticity," Mathematics, MDPI, vol. 8(9), pages 1-9, August.
    4. Li, Juan & Song, Weixing & Shi, Jianhong, 2015. "Parametric bootstrap simultaneous confidence intervals for differences of means from several two-parameter exponential distributions," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 39-45.
    5. Kharrati-Kopaei, Mahmood & Malekzadeh, Ahad & Sadooghi-Alvandi, Mohammad, 2013. "Simultaneous fiducial generalized confidence intervals for the successive differences of exponential location parameters under heteroscedasticity," Statistics & Probability Letters, Elsevier, vol. 83(6), pages 1547-1552.
    6. Singh, Parminder & Singh, Navdeep, 2013. "Simultaneous confidence intervals for ordered pairwise differences of exponential location parameters under heteroscedasticity," Statistics & Probability Letters, Elsevier, vol. 83(12), pages 2673-2678.

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