A new class of random vector entropy estimators and its applications in testing statistical hypotheses

By M. N. Goria, Nikolai N. Leonenko, V. Mergel, P. N. Inverardi. 2005

198 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Finance, Statistics and Probability

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Citations in the corpus

Nonparametric Divergence Estimation with Applications to Machine Learning on Distributions (2011, methodology): “To estimate the L 2 divergence, we will borrow some ideas from Leonenko et al. (2008) and Goria et al. (2005), who considered Shannon and Rényi-α entropy estimation from a single sample.”
On the Estimation of alpha-Divergences (2011, unknown): “(2008a,b); Goria et al. (2005); Wang et al. (2009a). We are now ready to begin proving Theorem 20.”
Breaking the Bandwidth Barrier: Geometrical Adaptive Entropy Estimation (2016, background): “As noted in [18], such an assumption is common in the literature on consistency of k-NN estimators, where it has been implicitly assumed in existing analyses of entropy estimators including [9, 5, 12, 27], without explicitly stating that such assumptions are being made.”
Divergence Estimation for Multidimensional Densities Via $k$-Nearest-Neighbor Distances (2009, methodology): “Goria et al. [16] extended the -NN differential entropy estimator to -NN estimation, where can be any constant.”
Efficient multivariate entropy estimation via $k$-nearest neighbour distances (2016, background): “In statistical contexts, it is often the estimation of entropy that is of primary interest, for instance in goodness-of-fit tests of normality (Vasicek, 1976) or uniformity (Cressie, 1976), tests of independence (Goria et al., 2005), independent component analysis (Miller and Fisher, 2003) and featu”
On the Estimation of α-Divergences (2011, methodology): “(2008a,b); Goria et al. (2005); Wang et al. (2009a). We are now ready to begin proving Theorem 20.”
A NEW ESTIMATOR OF ENTROPY (2010, background): “See for example Esteban et al. (2001), Park (2003), Choi et al. (2004), Goria et al. (2005), Choi (2008) and Alizadeh Noughabi and Arghami (2010).”
Causality detection based on information-theoretic approaches in time series analysis (2007, background): “Goria et al. [87] presented a simulation study showing that for many distribution families used in statistics, the hypothesis of asymptotic normal distribution of the nearest neighbor estimator seems to be acceptable (for Beta, Cauchy, Gamma, Laplace and Student t -distributions).”
Support Distribution Machines (2012, background): “, 2008), Shannon entropy (Goria et al., 2005), KL divergence (Wang et al.”
A Non-parametric Bayesian Network Prior of Human Pose (2013, unknown): “A more general class of entropy estimators including the one above was shown to be asymptotically unbiased and consistent as N → ∞ in [8].”
Empirical estimation of entropy functionals with confidence (2010, methodology): “The BPI estimator is designed to automatically incorporate boundary correction, without requiring prior knowledge of the support of the density.”
Parametric Bayesian Estimation of Differential Entropy and Relative Entropy (2010, background): “Other variants of nearest-neighbor differential entropy estimators have also been proposed and analyzed [10,11].”
Estimation of Renyi Entropy and Mutual Information Based on Generalized Nearest-Neighbor Graphs (2010, methodology): “A variant of these estimators, where each sample point is connected to its k -th nearest neighbor only, were recently studied by Goria et al. (2005) for Shannon entropy estimation ( i.e. the special case α = 1 ) and Leonenko et al. (2008) for R´enyi α -entropy estimation.”