Estimating the variance of Shannon entropy

The statistical analysis of data stemming from dynamical systems, including, but not limited to, time series, routinely relies on the estimation information theoretical quantities, most notably Shannon entropy. To this purpose, possibly widespread tool is provided by so-called plug-in estimator, whose properties in terms bias and variance were investigated since first decade after publication Shannon's seminal works. In case an underlying multinomial distribution, while can be evaluated knowing support set size, far more elusive. aim present work to investigate, case, estimator a parameter that describes We then exactly determine probability distributions maximize parameter. results presented here allow upper limits uncertainty entropy assessments under hypothesis memoryless stochastic processes.