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Abstract:
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Linear relationship among random variables has been fully explored in the past. This paper looks into dependence of one group of random variables upon another group of random variables using (conditional) entropy. A new measurement of range between zero and one, called K-dependence coefficient or dependence coefficient, is defined using (conditional) entropy. This paper shows that the dependence measured by K-dependence coefficient includes both linear and non-linear dependence between two groups of random variables. I.e. K-dependence coefficient totally measures the dependence, not part of the dependence, between the two groups of random variables. Furthermore, the concept of K-dependence coefficient is extended by defining Partial K-dependence coefficient and semi-partial K-dependence coefficient. Properties of partial and semi-partial K-dependence coefficients are also explored.
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