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Consider the problem of estimating the Shannon entropy of a distribution over $k$ elements from $n$ independent samples.
The relation between the number of species and the number of individuals in a random sample of an animal population
Ronald A Fisher, A Steven Corbet, and Carrington B Williams · 1943
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The population frequencies of species and the estimation of population parameters
Irwin J. Good · 1953
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Note on the bias of information estimates
George A. Miller · 1955
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A statistical problem arising in the theory of detection of signals in the presence of noise in a multi-channel system and leading to stable distribution laws
R.L. Dobrushin · 1958
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On a statistical estimate for the entropy of a sequence of independent random variables
G.P. Basharin · 1959
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Theory of approximation of functions of a real variable
Aleksandr Filippovich Timan · 1963
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Approximating discrete probability distributions with dependence trees
C.K. Chow and C.N. Liu · 1968
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Optimization by vector space methods
David G. Luenberger · 1969
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The statistical estimation of entropy in the non-parametric case
B. Harris · 1975
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Orthogonal polynomials
G. Szegö · 1975
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Estimating the number of unseen species: How many words did shakespeare know?
Bradley Efron and Ronald Thisted · 1976
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Minimum chi-square, not maximum likelihood! (with discussion)
Joseph Berkson · 1980
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Optimal rates of convergence for nonparametric estimators
Charles J. Stone · 1980
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Information Theory: Coding Theorems for Discrete Memoryless Systems
Imre Csiszár and János Körner · 1982
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Maximum likelihood and decision theory
Bradley Efron · 1982
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Mathematical theory of statistics: Statistical experiments and asymptotic decision theory
Helmut Strasser · 1985
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Asymptotic methods in statistical decision theory
L. Le Cam · 1986
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An efron-stein inequality for nonsymmetric statistics
J Michael Steele · 1986
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Some problems on nonparametric estimation in gaussian white noise
I.A. Ibragimov, A.S. Nemirovskii, and R.Z. Khas’minskii · 1987
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Geometrizing rates of convergence, II
David L. Donoho and Richard C. Liu · 1991
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Constructive approximation
Ronald A. DeVore and George G. Lorentz · 1993
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Reliability of spike timing in neocortical neurons
Zachary F Mainen and Terrence J Sejnowski · 1995
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An entropy estimator algorithm and telecommunications applications
Nina T. Plotkin and Abraham J. Wyner · 1996
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The structure and precision of retinal spike trains
Michael J. Berry, David K. Warland, and Markus Meister · 1997
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Reproducibility and variability in neural spike trains
Rob R. de Ruyter van Steveninck, Geoffrey D. Lewen, Steven P. Strong, Roland Koberle, and William Bialek · 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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Spikes: Exploring the Neural Code
Fred Rieke, William Bialek, David Warland, and Rob de Ruyter van Steveninck · 1999
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Asymptotic statistics
Aad W. Van der Vaart · 2000
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Testing composite hypotheses, Hermite polynomials and optimal estimation of a nonsmooth functional
T.T. Cai and M. G. Low · 2011
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Rational approximation of real functions
Penco Petrov Petrushev and Vasil Atanasov Popov · 2011
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Estimating the unseen: an n / log ( n ) n/\log(n) -sample estimator for entropy and support size, shown optimal via new CLTs
Gregory Valiant and Paul Valiant · 2011
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The power of linear estimators
Gregory Valiant and Paul Valiant · 2011
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Probability estimation in the rare-events regime
Aaron B Wagner, Pramod Viswanath, and Sanjeev R Kulkarni · 2011
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Estimation of the entropy based on its polynomial representation
Martin Vinck, Francesco P. Battaglia, Vladimir B. Balakirsky, A.J. Han Vinck, and Cyriel M.A. Pennartz · 2012
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Convergence properties of functional estimates for discrete distributions
András Antos and Ioannis Kontoyiannis · 2001
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Entropy, entropy rate, and pattern classification as tools to typify complexity in short heart period variability series
A. Porta, S. Guzzetti, N. Montano, R. Furlan, M. Pagani, A. Malliani, and S. Cerutti · 2001
Cited alongside, same era.
How to achieve minimax expected Kullback-Leibler distance from an unknown finite distribution
Dietrich Braess, Jürgen Forster, Tomas Sauer, and Hans U Simon · 2002
Cited alongside, same era.
On tractable approximations of randomly perturbed convext constaints
A. Nemirovski · 2003
Cited alongside, same era.
Estimation of entropy and mutual information
Liam Paninski · 2003
Cited alongside, same era.
Universal compression of memoryless sources over unknown alphabets
Alon Orlitsky, Narayana P Santhanam, and Junan Zhang · 2004
Cited alongside, same era.
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A sharp estimate of the binomial mean absolute deviation with applications
Daniel Berend and Aryeh Kontorovich · 2013
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Universal estimation of directed information
Jiantao Jiao, Haim H Permuter, Lei Zhao, Young-Han Kim, and Tsachy Weissman · 2013
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Classification of homogeneous data with large alphabets
B.G. Kelly, A.B. Wagner, T. Tularak, and P. Viswanath · 2013
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Efficient methods to compute optimal tree approximations of directed information graphs
Christopher J Quinn, Negar Kiyavash, and Todd P Coleman · 2013
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Estimating the unseen: Improved estimators for entropy and other properties
Paul Valiant and Gregory Valiant · 2013
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Private communication, Oct. 2014
J. Jiao · 2014
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Maximum likelihood estimation of functionals of discrete distributions
Jiantao Jiao, Kartik Venkat, Yanjun Han, and Tsachy Weissman · 2014
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The complexity of estimating Rényi entropy
Jayadev Acharya, Alon Orlitsky, Ananda Theertha Suresh, and Himanshu Tyagi · 2015
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Efficiently learning ising models on arbitrary graphs
Guy Bresler · 2015
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Adaptive estimation of Shannon entropy
Yanjun Han, Jiantao Jiao, and Tsachy Weissman · 2015
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Does Dirichlet prior smoothing solve the Shannon entropy estimation problem?
Yanjun Han, Jiantao Jiao, and Tsachy Weissman · 2015
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Minimax estimation of functionals of discrete distributions
Jiantao Jiao, Kartik Venkat, Yanjun Han, and Tsachy Weissman · 2015
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Chebyshev polynomials, moment matching, and optimal estimation of the unseen
Yihong Wu and Pengkun Yang · 2015
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Optimal entropy estimation on large alphabets via best polynomial approximation
Yihong Wu and Pengkun Yang · 2015
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Optimal property estimation on large alphabets: fundamental limits and fast algorithms
Pengkun Yang · 2016
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