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

• Published in: Statistics & probability letters Vol. 81; no. 10; pp. 1507 - 1517
• Main Authors: Maurya, Vishal, Goyal, Anju, Gill, Amar Nath
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.10.2011; Elsevier
• Series: Statistics & Probability Letters
• Subjects: Bonferroni inequality; Exact sciences and technology; Experimental design; General topics; Heteroscedasticity; Mathematics; Multivariate analysis; One-stage procedure; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Statistics; Two-parameter exponential distribution; Two-parameter exponential distribution Two-stage procedure One-stage procedure Bonferroni inequality Heteroscedasticity; Two-stage procedure; Two-stage procedure; Bonferroni inequality; Two-parameter exponential distribution; One-stage procedure; Heteroscedasticity; Rank statistic; Data analysis; Critical value; Exponential distribution; Probability theory; Gaussian distribution; Location parameter; Statistical estimation; Multiple comparison; Confidence interval; Statistical method; Statistical test; Simulation; Experimental design; Subset selection
• ISSN: 0167-7152; 1879-2103
• DOI: 10.1016/j.spl.2011.05.010

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.