Linear Contrasts in Experimental Design with Non-Identical Error Distributions

Şenoğlu, Birdal; Tiku, M. L.

doi:10.1002/1521-4036(200204)44:3<359::aid-bimj359>3.0.co;2-k

Cited by 15 publications

(10 citation statements)

References 17 publications

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“…According to the results presented in Senoglu and Tiku, 2002). This result is consistent with the simulation results presented in Table 2.…”

Section: Results Of Quantiles Estimates For Wind Speed Datamentioning

confidence: 97%

Estimation of the Lower and Upper Quantiles of Gumbel Distribution: An Application to Wind Speed Data

Aydin¹

2018

Appl. Ecol. Env. Res.

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Aydin: Estimation of the lower and upper quantiles of Gumbel distribution: an application to wind speed data - Abstract. In this paper, we consider different estimators of the quantiles of two-parameter Gumbel distribution. We use methodologies known as maximum likelihood, modified maximum likelihood and probability weighted moment to obtain the estimators of the quantiles. We compare the performances of the estimators with respect to bias and mean square error criteria via Monte Carlo simulation study. Their robustness properties are also examined in the presence of data anomalies. In the real data analysis part of the study, the seasonal maximum daily wind speed data from Sinop station (Turkey) in 2015 is considered. It is modelled by using two-parameter Gumbel distribution and analysed to compare the performances of the methodology presented in the study. All in all, the results of simulations and the real data application show that the maximum likelihood and modified maximum likelihood estimators, which have similar performance, provide better performance than the probability weighted moment estimator does in both obtaining estimates of the quantiles of Gumbel distribution and modelling of the data for almost all cases.

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“…According to the results presented in Senoglu and Tiku, 2002). This result is consistent with the simulation results presented in Table 2.…”

Section: Results Of Quantiles Estimates For Wind Speed Datamentioning

confidence: 97%

Estimation of the Lower and Upper Quantiles of Gumbel Distribution: An Application to Wind Speed Data

Aydin¹

2018

Appl. Ecol. Env. Res.

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“…Conclusions LS estimators of the main effects and interaction(s) are used traditionally for the 2 k factorial design. However, efficiencies of the LS estimators are low and they are not robust to departures from normality, see, for example, Ş enoglu & Tiku (2001Tiku ( , 2002 in the context of experimental design. In this paper, we derived estimators and developed new test statistics for testing the main effects and interaction(s) when the error terms are Weibull W(p,s).…”

Section: Future Workmentioning

confidence: 96%

Robust 2^kfactorial design with Weibull error distributions

Şenoğlu

2005

Journal of Applied Statistics

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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 2 k factorial design when the distribution of error terms are Weibull W(p,s). From the methodology of modified likelihood, we develop robust and efficient estimators for the parameters in 2 k 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.

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“…Solving such equations by iteration is very problematic (Punhenpura and Sinha 1986;Vaughan 1992;Senoglu and Tiku 2002). Therefore, the MLE are elusive.…”

Section: Estimationmentioning

confidence: 99%