Online Program

Thursday, February 18
PS1 Poster Session 1 & Opening Mixer sponsored by SAS Thu, Feb 18, 5:30 PM - 7:00 PM
Ballroom Foyer

Introduction of Generalized Weighted Correlation Coefficients and Their Properties (303258)

Hao Chen, Stony Brook University 
Song Wu, Stony Brook University 
Jie Yang, Stony Brook University 
*Mengru Zhang, Stony Brook University 

Keywords: Pearson’s correlation coefficient, Spearman’s rank correlation coefficient, weighted correlation coefficient

Correlation coefficients are popularly used to describe the relationship between two continuous variables, x and y. A weighted correlation coefficient uses weights to represent the differing degrees of importance of each data pair. A generalized situation is to allow different weights for x and y. For example, in brain imaging data, a region of interest (ROI) level binding potential measurement is estimated from voxels in that ROI along with standard error to reflect the variation in voxel-level measurements and hence x and y have different weights. In this presentation, a generalized weighted correlation coefficient that could be applied in the situations that either x or y or both measurements have their own weights will be introduced. It will be compared with the commonly used weighted correlation coefficient where each pair of (x,y) shares the same weight. It can also be extended to be rank-based. Asymptotic properties of the generalized weighted correlation coefficient will be also investigated and compared with bootstrapping results. The application of such weighted correlation coefficients are illustrated using both simulations and different real data sets.