Kendall's Tau for non-independent data
LE3 .A278 2021
Bachelor of Science
Mathematics and Statistics
Mathematics & Statistics
Kendall’s Tau is a non-parametric U-statistic used on bivariate data that measures whether or not these two variables are independent and, if not independent, assesses the type and degree of dependency that exists between them based on the concordance (and discordance) structure of the data. One of the assumptions of Kendall’s Tau procedure requires that the paired observations be mutually independent and identically distributed (iid) according to some, known or unknown, continuous distribution. Requiring this assumption causes certain issues when exploring certain datasets with non-iid structures, particularly, bivariate time-series data. The purpose of this thesis is to examine the behaviour of Kendall’s Tau when the iid assumption is relaxed to include weakly stationary time-series data. We will discuss different methods to find a reliable variance estimate to construct accurate confidence intervals when dealing with these types of data. Additionally, we will determine which one of these estimates are best given a certain situation looking at both the advantages and disadvantages to all proposed estimates.
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