A recursive Renyi's entropy estimator

Estimating the entropy of a sample set is required, in solving numerous learning scenarios involving information theoretic optimization criteria. A number of entropy estimators are available in the literature; however, these require a batch of samples to operate on in order to yield an estimate. We derive a recursive formula to estimate Renyi's (1970) quadratic entropy on-line, using each new sample to update the entropy estimate to obtain more accurate results in stationary situations or to track the changing entropy of a signal in nonstationary situations.