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Dependence Orders

In: Stochastic Comparisons with Applications

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  • Subhash C. Kochar

    (Portland State University, Fariborz Maseeh Department of Mathematics and Statistics)

Abstract

Dependence among random variables is one of the most widely studied topics in the literature with lots of applications in diverse areas. Pearson’s coefficient of correlation, which is the traditional measure of dependence between random variables, has several limitations. It can detect only linear relationships between random variables. Several other notions and measures of dependence have been proposed and studied in the literature. After reviewing the various notions of monotone dependence including the likelihood ratio dependence, the monotone regression dependence, the right tail increasing (RTI), and the positive quadrant dependence, the corresponding partial orders to compare the strength of dependence within the components of random vectors of the same dimension are discussed. These include discussion of the more concordance order, the more regression dependence, and the more RTI orders. We also review some measures of dependence satisfying the Scarsini axioms (Stochastica 8:201–218, 1984) which include the Kendall’s tau, the Spearman’s rho, and the Gini’s measures of concordance. These are demonstrated with the help of several examples. Towards the end, some nonparametric tests for independence are discussed. The emphasis is on the techniques and ideas behind their developments rather than on data analysis.

Suggested Citation

  • Subhash C. Kochar, 2022. "Dependence Orders," Springer Books, in: Stochastic Comparisons with Applications, chapter 0, pages 115-137, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-12104-3_5
    DOI: 10.1007/978-3-031-12104-3_5
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