Abstract:In this note we consider the estimation of the differential entropy of a~probability density function. We propose a new adaptive estimator based on a plug-in approach and wavelet methods. Under the mean $\mathbb{L}_p$ error, $p\ge 1$, this estimator attains fast rates of convergence for a wide class of functions. We present simulation results in order to support our theoretical findings.
Keywords: entropy; wavelet estimation; rate of convergence; mean $\mathbb{L}_p$ error
DOI: DOI 10.14712/1213-7243.2015.191
AMS Subject Classification: 62G07 62G20