Abstract
ABSTRACTIn multivariate statistics, the linear relationship among random variables has been fully explored in the past. This paper looks into the dependence of one group of random variables on another group of random variables using (conditional) entropy. A new measure, called the K‐dependence coefficient or dependence coefficient, is defined using (conditional) entropy. This paper shows that the K‐dependence coefficient is a measure of the degree of dependence of one group of random variables on another group of random variables. The dependence measured by the K‐dependence coefficient includes both linear and nonlinear dependencies between two groups of random variables. Therefore, the K‐dependence coefficient measures the total degree of dependence and not just the linear component of the dependence between the two groups of random variables. Furthermore, the concept of the K‐dependence coefficient is extended by defining the partial K‐dependence coefficient and the semipartial K‐dependence coefficient. Properties of partial and semipartial K‐dependence coefficients are also explored.
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