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Robust 2k factorial design with Weibull error distributions

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  • Bi-super-˙rdal Senoğlu

Abstract

It is well known that the least squares method is optimal only if the error distributions are normally distributed. However, in practice, non-normal distributions are more prevalent. If the error terms have a non-normal distribution, then the efficiency of least squares estimates and tests is very low. In this paper, we consider the 2k factorial design when the distribution of error terms are Weibull W(p,σ). From the methodology of modified likelihood, we develop robust and efficient estimators for the parameters in 2k factorial design. F statistics based on modified maximum likelihood estimators (MMLE) for testing the main effects and interaction are defined. They are shown to have high powers and better robustness properties as compared to the normal theory solutions. A real data set is analysed.

Suggested Citation

  • Bi-super-˙rdal Senoğlu, 2005. "Robust 2k factorial design with Weibull error distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(10), pages 1051-1066.
    • Handle: RePEc:taf:japsta:v:32:y:2005:i:10:p:1051-1066
    DOI: 10.1080/02664760500165099
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    Cited by:

    1. Tiku, Moti L. & Senoglu, Birdal, 2009. "Estimation and hypothesis testing in BIB design and robustness," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3439-3451, July.
    2. Tiku, Moti L. & Islam, M. Qamarul & Sazak, Hakan S., 2008. "Estimation in bivariate nonnormal distributions with stochastic variance functions," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1728-1745, January.
    3. Tiku, Moti L. & Sürücü, Baris, 2009. "MMLEs are as good as M-estimators or better," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 984-989, April.

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