Robustness of adaptive methods for non-normal data : skewed normal data as an example

مقدم أطروحة جامعية

Abu Shuraydah, Rima Musa Abu Bakr

مشرف أطروحة جامعية

al-Umari, Amir Ibrahim F.
al-Zubi, Luayy Muhammad A.

أعضاء اللجنة

al-Khazailah, Ahmad Muhammad
al-Zughul, Raid Ahmad

الجامعة

جامعة آل البيت

الكلية

كلية العلوم

القسم الأكاديمي

قسم الرياضيات

دولة الجامعة

الأردن

الدرجة العلمية

ماجستير

تاريخ الدرجة العلمية

2013

الملخص الإنجليزي

Variances for estimators of means and regression coefficients are usually high when fitting two-stage sampling because of intra-class homogeneity.

To decide the proper way of allowing for intra-class correlation using sample data, this thesis develops and evaluates adaptive strategies for designing and analyzing two-stage surveys. The analysis approach to estimate means and regression coefficients is based on fitting a linear regression model.

One method for allowing for clustering in fitting a linear regression model is to use a linear mixed model with two levels.

It is possibly suitable to ignore clustering and use a single level model if the estimated intra-class correlation is close to zero. This thesis tested and evaluated an adaptive method for estimating the variances of estimated regression coefficients in case of non-normal data.

The strategy is based on testing the null hypothesis that the random effect variance component is zero.

If this hypothesis is not rejected the estimated variances of estimated regression coefficients are extracted from the one-level linear model.

Otherwise, the estimated variance is based on the linear mixed model, or, alternatively the Huber-White robust variance estimator is used. The skewed-normal data will be used to assess the robustness of the adaptive method if the assumption of normality is not justified.

The adaptive methods are evaluated by simulation using skewed-normal data, with equal and unequal numbers of observations per cluster. Extreme designs with 5 or less PSUs have to be avoided as the simulation revealed.

For these extreme designs, most methods perform poorly, including the adaptive methods and the linear mixed model, due to the difficulty of appropriately defining the degrees of freedom for this model. Apart from these extreme designs, the adaptive strategy is found to perform acceptably well, resulting in simpler analysis and slightly shorter confidence intervals.

التخصصات الرئيسية

الرياضيات

الموضوعات

• التحليل متعدد المتغيرات

عدد الصفحات

60

قائمة المحتويات

• APA
• MLA
• AMA

لغة النص

الإنجليزية

نوع البيانات

رسائل جامعية

رقم السجل

BIM-420931