Date of Graduation

8-2023

Document Type

Thesis

Degree Name

Master of Science in Mathematics (MS)

Degree Level

Graduate

Department

Mathematical Sciences

Advisor/Mentor

Avishek Chakraborty

Committee Member

Mark E. M Arnold

Second Committee Member

Qingyang Q Zhang

Keywords

Correlation;Non-monotone

Abstract

Evaluating association between variables is often of interest by many researchers. To serve this purpose, different association measures have been developed. However, type of relation between variables affects the degree of relationship. Hence, detection of the rela- tionship between variables is germane to measuring the correlation coefficient. With that mindset, here we explored six non-monotonic measure of association techniques and com- pared them with three classical approaches. Due to inconsistency in definition and range of different techniques, it is not feasible to compare the correlation estimates as their nature of variability differ. Therefore, we used permutation test based on Monte Carlo approximation for testing independence. We paired the correlation estimates along with the p-value for deciding strength of association between variables. At first, we explored and compared the association measures on twelve distinct simulation models under diverse scenario segregated by three sample sizes and three noise levels. In addition, we assessed the computational time and peak memory (RAM) usage during computations for each of these methods. Next, we applied all methods on Cape Floristic Region (CFR) data to capture association between four pairs of variable combinations with varying sample sizes. Overall, we found that, increasing sample size improves the performance of correlation measure. For any type of relationship, non-monotone measures were consistent in capturing association for large sample size. With respect to time and peak memory usage, we found two of the methods were not efficient.

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