Robustness of adaptive methods for non-normal data : skewed normal data as an example
Dissertant
Abu Shuraydah, Rima Musa Abu Bakr
Thesis advisor
al-Umari, Amir Ibrahim F.
al-Zubi, Luayy Muhammad A.
Comitee Members
al-Khazailah, Ahmad Muhammad
al-Zughul, Raid Ahmad
University
Al albayt University
Faculty
Faculty of Sciences
Department
Department of Mathematics
University Country
Jordan
Degree
Master
Degree Date
2013
English Abstract
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.
Main Subjects
Topics
No. of Pages
60
Table of Contents
Table of contents.
Abstract.
Chapter One : Introduction and literature review.
Chapter Two : Robustness of adaptive estimators based on skew normal distribution for balanced data.
Chapter Three : Robustness of adaptive estimators based on skew normal distribution for unbalanced data.
Chapter Four : Conclusions.
References.
American Psychological Association (APA)
Abu Shuraydah, Rima Musa Abu Bakr. (2013). Robustness of adaptive methods for non-normal data : skewed normal data as an example. (Master's theses Theses and Dissertations Master). Al albayt University, Jordan
https://search.emarefa.net/detail/BIM-420931
Modern Language Association (MLA)
Abu Shuraydah, Rima Musa Abu Bakr. Robustness of adaptive methods for non-normal data : skewed normal data as an example. (Master's theses Theses and Dissertations Master). Al albayt University. (2013).
https://search.emarefa.net/detail/BIM-420931
American Medical Association (AMA)
Abu Shuraydah, Rima Musa Abu Bakr. (2013). Robustness of adaptive methods for non-normal data : skewed normal data as an example. (Master's theses Theses and Dissertations Master). Al albayt University, Jordan
https://search.emarefa.net/detail/BIM-420931
Language
English
Data Type
Arab Theses
Record ID
BIM-420931
