ROBUSTNESS PROPERTIES OF GENERALIZED CORRELATION COEFFICIENTS, WITH APPLICATIONS TO CROSS-OVER DESIGNS
Open Access
- Author:
- Chen, Yi-Ju
- Graduate Program:
- Statistics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- October 02, 2006
- Committee Members:
- Vernon Michael Chinchilli, Committee Chair/Co-Chair
Donald Richards, Committee Member
Rana Arnold, Committee Member
Tonya Sharp King, Committee Member
Bruce G. Lindsay, Committee Member - Keywords:
- Generalized Correlation Coefficient
Cross-Over Designs
Influence Function
Robustness - Abstract:
- To date, correlation coefficients have been the most utilized statistical measures in many fields for investigating the presence of a relationship between two variables or among several variables. However, presently in the literature, there is a lack of discussion of correlation coefficients within the context of cross-over designs. Therefore, the basic stage we are studying in this dissertation is the development of a `class' of correlation coefficients, henceforth below called `generalized correlation coefficient', which contains Pearson and Kendall correlations as two special cases, and can be adapted to cross-over designs. Pioneer work for this approach has been done by Chinchilli et al. (2005) for the simplest case, the basic 2¡Ñ2 cross-over designs, but the authors do not pursue the robustness properties of the generalized correlation coefficient. Thus, an objective of this dissertation is to derive the associated influence function and then address robustness behaviors of the generalized correlation coefficient. On the other hand, we also broaden the work of Chinchilli et al. (2005), allowing for the generalized correlation coefficient being applicable to more complex cross-over designs which are uniform within sequences. We develop the corresponding asymptotic theory and influence function in this direction. Moreover, contours of constant influence for the generalized correlation coefficient are introduced as well in this dissertation and are demonstrated to be useful for detecting unusual observations in a given data set.