Interval Estımatıon Based On Robust Estımators For The Dıfference Of Two Independent Populatıon Varıances

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Thesis Type: Doctorate

Institution Of The Thesis: Gazi University, Fen Bilimleri Enstitüsü, İSTATİSTİK ANABİLİM DALI, Turkey

Approval Date: 2017

Thesis Language: Turkish

Student: HAYRİYE ESRA AKYÜZ

Supervisor: HAMZA GAMGAM

Open Archive Collection: AVESIS Open Access Collection

Abstract:

In random experiments, most analyses are based on interpretation of the difference between the means of experiment and control groups. Therefore, studying the difference between the variances of the experiment and control groups may also be useful in interpreting the analysis results. In estimation of variances of normal populations, sample variance estimator is used. It is known that sample variance estimator does not display robust statistics features in the estimation of nonnormal population variance and the coverage probabilities of the confidence intervals obtained with this estimator have much lower values compared to the nominal confidence interval. In such cases, it is necessary to use robust estimators for estimation of population variance. In this study, it was proposed that confidence interval methods based on robust estimators were used to estimate the difference of variances of two nonnormal populations. This confidence intervals were compared in terms of coverage probabilities and average length widths under same simulation conditions. These estimators are Winsorized and Trimmed variances. In addition, they are sample variance estimators based on binary distances, median of binary distances and median of the absolute deviations from the median. Firstly, the distributions of estimators were determined with the simulation study. Therefore, confidence intervals based on this estimators for the difference of the variances of two nonnormally populations were compared in terms of coverage probabilities and average interval widths. According to simulation study, it was determined that the coverage probabilities of confidence intervals based on the estimators were very close to the nominal confidence level in any case. However, it was seen that the average interval widths of confidence intervals obtained with sample variance estimator based on Trimmed Mean were narrower compared to the average interval widths of confidence intervals obtained with other sample variance estimators. The largest average interval widths were obtained with estimator based on median of the absolute deviations from the median. In addition, it was determined that these results were the same when the Type I error was different.