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We consider the distinct elements problem, where the goal is to estimate the number of distinct colors in an urn containing $ k $ balls based on $n$ samples drawn with replacements.
The relation between the number of species and the number of individuals in a random sample of an animal population
Ronald Aylmer Fisher, A Steven Corbet, and Carrington B Williams · 1943
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Calculus of finite differences
Charles Jordan · 1947
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On the estimation of the number of classes in a population
Leo A Goodman · 1949
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The population frequencies of species and the estimation of population parameters
Irving J Good · 1953
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The condition of the finite segments of the Hilbert matrix
John Todd · 1954
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Asymptotic development of the Stirling numbers of the first kind
L Moser and M Wyman · 1958
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Probability inequalities for sums of bounded random variables
W. Hoeffding · 1963
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Theory of approximation of functions of a real variable
Aleksandr Filippovich Timan · 1963
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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?
B. Efron and R. Thisted · 1976
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Estimation of the number of connected components in a graph by using a sampled subgraph
Ove Frank · 1978
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Posterior moments of the number of species in a finite population and the posterior probability of finding a new species
Bruce M Hill · 1979
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Estimation of the size of a coinage: A survey and comparison of methods
Warren W Esty · 1986
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Statistical estimators for relational algebra expressions
Wen-Chi Hou, Gultekin Ozsoyoglu, and Baldeo K Taneja · 1988
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Vandermonde matrices on the circle: spectral properties and conditioning
Antonio Córdova, Walter Gautschi, and Stephan Ruscheweyh · 1990
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How (un) stable are Vandermonde systems
Walter Gautschi · 1990
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On estimating the size of projections
Jeffrey F Naughton and S Seshadri · 1990
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Classical orthogonal polynomials of a discrete variable
Arnold F Nikiforov, Vasilii B Uvarov, and Sergei K Suslov · 1991
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Estimating the number of classes via sample coverage
Anne Chao and Shen-Ming Lee · 1992
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From the species problem to a general coverage problem via a new interpretation
Shaw-Hwa Lo · 1992
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Estimating the number of species: a review
John Bunge and M Fitzpatrick · 1993
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Asymptotic estimates of Stirling numbers
Nico M Temme · 1993
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On the shape–from–moments problem and recovering edges from noisy Radon data
Alexander Goldenshluger and Vladimir Spokoiny · 2004
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Estimating entropy on m m bins given fewer than m m samples
Liam Paninski · 2004
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Probability and computing: Randomized algorithms and probabilistic analysis
Michael Mitzenmacher and Eli Upfal · 2005
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Hyperloglog: The analysis of a near-optimal cardinality estimation algorithm
Philippe Flajolet, Éric Fusy, Olivier Gandouet, and Frédéric Meunier · 2007
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Strong lower bounds for approximating distribution support size and the distinct elements problem
Sofya Raskhodnikova, Dana Ron, Amir Shpilka, and Adam Smith · 2009
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Introduction to Nonparametric Estimation
A.B. Tsybakov · 2009
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Yang Chen and Nigel Lawrence · 1999
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Super-resolution, the recovery of missing samples and Vandermonde matrices on the unit circle
PJSG Ferreira · 1999
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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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The condition number of real Vandermonde, Krylov and positive definite Hankel matrices
Bernhard Beckermann · 2000
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Towards estimation error guarantees for distinct values
Moses Charikar, Surajit Chaudhuri, Rajeev Motwani, and Vivek Narasayya · 2000
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Asymptotic estimates for generalized Stirling number
R Chelluri, LB Richmond, and NM Temme · 2000
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An optimal algorithm for the distinct elements problem
Daniel M Kane, Jelani Nelson, and David P Woodruff · 2010
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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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Testing symmetric properties of distributions
Paul Valiant · 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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Algorithmic Approaches to Statistical Questions
Gregory Valiant · 2012
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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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Super-resolution, extremal functions and the condition number of Vandermonde matrices
Ankur Moitra · 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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Minimax rates of entropy estimation on large alphabets via best polynomial approximation
Yihong Wu and Pengkun Yang · 2016
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