Nonparametric estimation of the measure of functional dependence

In this paper, we propose a beta kernel estimator to measure functional dependence (MFD). The MFD not only can measure the strength of linear or monotonic relationships, but it is also suitable for more complicated functional dependence. We derive the asymptotic distribution of the proposed estimator and then use several simulated examples to compare our estimator with the traditional measures. Our simulation results demonstrate that beta kernel provides high accuracy in estimation. A real data example is also given to illustrate one possible application of the new estimator.