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We analyze the Kozachenko--Leonenko (KL) nearest neighbor estimator for the differential entropy.
Asymptotically efficient estimation of nonlinear functionals
Boris Ya Levit · 1978
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Multivariate k k -nearest neighbor density estimates
YP Mack and Murray Rosenblatt · 1979
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The jackknife estimate of variance
Bradley Efron and Charles Stein · 1981
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Limit theorems for sums of general functions of m-spacings
Peter Hall · 1984
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Estimation of integrated squared density derivatives
Peter Hall and James Stephen Marron · 1987
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Sample estimate of the entropy of a random vector
LF Kozachenko and Nikolai N Leonenko · 1987
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Estimating integrated squared density derivatives: sharp best order of convergence estimates
Peter J Bickel and Ya’acov Ritov · 1988
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Estimation of entropy and other functionals of a multivariate density
Harry Joe · 1989
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Minimax quadratic estimation of a quadratic functional
David L Donoho and Michael Nussbaum · 1990
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On the estimation of quadratic functionals
Jianqing Fan · 1991
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On problems of adaptive estimation in white gaussian noise
Oleg V Lepski · 1992
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Estimating functionals related to a density by a class of statistics based on spacings
Bert Van Es · 1992
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On the estimation of entropy
Peter Hall and Sally C Morton · 1993
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Using mutual information for selecting features in supervised neural net learning
R. Battiti · 1994
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Estimation of integral functionals of a density
Lucien Birgé and Pascal Massart · 1995
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Estimating nonquadratic functionals of a density using haar wavelets
Gérard Kerkyacharian and Dominique Picard · 1996
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Efficient estimation of integral functionals of a density
Béatrice Laurent · 1996
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Root- n n consistent estimators of entropy for densities with unbounded support
Alexandre B Tsybakov and EC Van der Meulen · 1996
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Nonparametric entropy estimation: An overview
Jan Beirlant, Edward J Dudewicz, László Györfi, and Edward C Van der Meulen · 1997
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On estimation of the L r L_{r} norm of a regression function
Oleg Lepski, Arkady Nemirovski, and Vladimir Spokoiny · 1999
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Topics in non-parametric
Arkadi Nemirovski · 2000
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A note on nonparametric estimation of linear functionals
T Tony Cai and Mark G Low · 2003
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Fast binary feature selection with conditional mutual information
F. Fleuret · 2004
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Estimating mutual information
Alexander Kraskov, Harald Stögbauer, and Peter Grassberger · 2004
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Nonquadratic estimators of a quadratic functional
T Tony Cai and Mark G Low · 2005
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On boundary correction in kernel density estimation
Rhoana J Karunamuni and Tom Alberts · 2005
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Multivariate mutual information inspired by secret-key agreement
C. Chan, A. Al-Bashabsheh, J. B. Ebrahimi, T. Kaced, and T. Liu · 2015
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Measure theory and fine properties of functions
Lawrence Craig Evans and Ronald F Gariepy · 2015
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Nonparametric von Mises estimators for entropies, divergences and mutual informations
Kirthevasan Kandasamy, Akshay Krishnamurthy, Barnabas Poczos, Larry Wasserman, et al · 2015
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Lepski’s method and adaptive estimation of nonlinear integral functionals of density
Rajarshi Mukherjee, Eric Tchetgen Tchetgen, and James Robins · 2015
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Efficient multivariate entropy estimation via k k -nearest neighbour distances
Thomas B Berrett, Richard J Samworth, and Ming Yuan · 2016
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H. Peng, F. Long, and C. Ding · 2005
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A simple adaptive estimator of the integrated square of a density
Evarist Giné and Richard Nickl · 2008
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Higher order influence functions and minimax estimation of nonlinear functionals
James Robins, Lingling Li, Eric Tchetgen, and Aad van der Vaart · 2008
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Minimax estimation of the integral of a power of a density
Eric Tchetgen, Lingling Li, James Robins, and Aad van der Vaart · 2008
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Introduction to Nonparametric Estimation
A. Tsybakov · 2008
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On entropy estimation by m m -spacing method
Fidah El Haje Hussein and Yu Golubev · 2009
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Estimation of KL divergence between large-alphabet distributions
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Conditional dependence via shannon capacity: Axioms, estimators and applications
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Minimax rate-optimal estimation of divergences between discrete distributions
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On adaptive estimation of nonparametric functionals
Rajarshi Mukherjee, Eric Tchetgen Tchetgen, and James Robins · 2016
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Higher order estimating equations for high-dimensional models
James Robins, Lingling Li, Rajarshi Mukherjee, Eric Tchetgen Tchetgen, and Aad van der Vaart · 2016
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Finite-sample analysis of fixed- k k nearest neighbor density functional estimators
Shashank Singh and Barnabás Póczos · 2016
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On the kozachenko–leonenko entropy estimator
Sylvain Delattre and Nicolas Fournier · 2017
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Estimating mutual information for discrete-continuous mixtures
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Demystifying fixed k-nearest neighbor information estimators
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