Estimators of measures of complete dependence for random vectors

Abstract

In this dissertation, we provide a constuction method of an estimator for a measure of complete dependence. The measure is a measure of complete dependence between a random variable and a random vector which none of its estimator has been proposed. In this work, the estimators are constucted via plug-in method and kernel method. The aim of this dissertation is not only to find an estimator for the measure of complete dependence but also the sufficient conditions to guarantee that the esimator converges to the true value as the sample size tends to infinity. In addition, the constuction method can be applied to other measures of complete dependence as well.