Abstract
The key to probability density function (p.d.f.) estimation is the determination of optimal bandwidth of kernel density estimator (KDE). The typical optimization strategy is to use the unknown p.d.f. to solve the unknown bandwidth, i.e., taking the mean integrated squared error between the unknown p.d.f. and the estimated p.d.f. as the objective function and calculating the optimal bandwidth by minimizing the objective function. Unlike the existing KDEs, this paper proposes a new minimum entropy-based KDE (ME-KDE) which represents the objective function with the re-substitution entropy of given data set. Meanwhile, a new fixed-point iteration algorithm is designed efficiently to determine the optimal bandwidth. ME-KDE reduces the uncertainty when determining the optimal bandwidth and thus enhances the stability of p.d.f. estimation. The experimental results on univariate and multivariate probability distributions demonstrate the feasibility and effectiveness of ME-KDE.
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