Asymptotically Unbiased Estimation of A Nonsymmetric Dependence Measure Applied to Sensor Data Analytics and Financial Time Series

A fundamental concept frequently applied to statistical machine learning is the detection of dependencies between unknown random variables found from data samples. In previous work, we have introduced a nonparametric unilateral dependence measure based on Onicescu’s information energy and a kNN method for estimating this measure from an available sample set of discrete or continuous variables. This paper provides the formal proofs which show that the estimator is asymptotically unbiased and has asymptotic zero variance when the sample size increases. It implies that the estimator has good statistical qualities. We investigate the performance of the estimator for data analysis applications in sensor data analysis and financial time series.