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Le Cam's method (or the two-point method) is a commonly used tool for obtaining statistical lower bound and especially popular for functional estimation problems.
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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Asymptotically subminimax solutions of compound statistical decision problems
Herbert Robbins · 1951
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Minimax theorems
Ky Fan · 1953
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The number of new species, and the increase in population coverage, when a sample is increased
I.J. Good and G.H. Toulmin · 1956
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The minimum distance method
J. Wolfowitz · 1957
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Linear Operators: General theory
N. Dunford and J.T. Schwartz · 1958
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Nonparametric estimation from incomplete observations
Edward L Kaplan and Paul Meier · 1958
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Über das von Neumannsche minimax-theorem
Heinz König · 1968
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Convergence of estimates under dimensionality restrictions
L. Le Cam · 1973
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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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On the nonparametric estimation of a value of a linear functional in the Gaussian white noise
I.A. Ibragimov and R.Z. Has’minskii · 1984
Earlier work this paper cites.
Mathematical theory of statistics: Statistical experiments and asymptotic decision theory
Helmut Strasser · 1985
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Fundamentals of statistical exponential families with applications in statistical decision theory
L. D. Brown · 1986
Earlier work this paper cites.
On Fan’s minimax theorem
Jonathan M Borwein and D Zhuang · 1986
Earlier work this paper cites.
Asymptotic methods in statistical decision theory
Lucien Le Cam · 1986
Earlier work this paper cites.
Real and complex analysis
Walter Rudin · 1987
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Geometrizing rates of convergence, II
David L. Donoho and Richard C. Liu · 1991
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Estimating the number of classes via sample coverage
Anne Chao and Shen-Ming Lee · 1992
Cited alongside, same era.
Information bounds and nonparametric maximum likelihood estimation
Piet Groeneboom and Jon A Wellner · 1992
Cited alongside, same era.
Estimating the number of species: a review
John Bunge and M Fitzpatrick · 1993
Cited alongside, same era.
Statistical estimation and optimal recovery
David L Donoho · 1994
Cited alongside, same era.
Applications of the van Trees inequality: a Bayesian Cramér-Rao bound
R. D. Gill and B. Y. Levit · 1995
Cited alongside, same era.
A constrained risk inequality with applications to nonparametric functional estimation
L. D. Brown and M. G. Low · 1996
Cited alongside, same era.
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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Testing composite hypotheses, Hermite polynomials and optimal estimation of a nonsmooth functional
T. T. Cai and M. G. Low · 2011
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Convexity: An analytic viewpoint
Barry Simon · 2011
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Testing symmetric properties of distributions
Paul Valiant · 2011
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The power of linear estimators
Gregory Valiant and Paul Valiant · 2011
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Interval censored survival data: a review of recent progress
Jian Huang and Jon A Wellner · 1997
Cited alongside, same era.
Assouad, Fano, and Le Cam
Bin Yu · 1997
Cited alongside, same era.
Empirical bayes and compound estimation of normal means
Cun-Hui Zhang · 1997
Cited alongside, same era.
On estimation of the L r L_{r} norm of a regression function
Oleg Lepski, Arkady Nemirovski, and Vladimir Spokoiny · 1999
Cited alongside, same era.
Towards estimation error guarantees for distinct values
Moses Charikar, Surajit Chaudhuri, Rajeev Motwani, and Vivek Narasayya · 2000
Cited alongside, same era.
On choosing and bounding probability metrics
Alison L Gibbs and Francis Edward Su · 2002
Cited alongside, same era.
Restriction access
Zeev Dvir, Anup Rao, Avi Wigderson, and Amir Yehudayoff · 2012
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Algorithmic Approaches to Statistical Questions
Gregory Valiant · 2012
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Population recovery and partial identification
Avi Wigderson and Amir Yehudayoff · 2012
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Nonparametric estimation under shape constraints
Piet Groeneboom and Geurt Jongbloed · 2014
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Optimal adaptive estimation of linear functionals under sparsity
Olivier Collier, Laëtitia Comminges, Alexandre B Tsybakov, and Nicolas Verzelen · 2016
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Optimal prediction of the number of unseen species
Alon Orlitsky, Ananda Theertha Suresh, and Yihong Wu · 2016
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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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Minimax estimation of linear and quadratic functionals on sparsity classes
Olivier Collier, Laëtitia Comminges, and Alexandre B Tsybakov · 2017
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Sample complexity of population recovery
Y. Polyanskiy, A. T. Suresh, and Y. Wu · 2017
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Sample complexity of the distinct element problem
Yihong Wu and Pengkun Yang · 2018
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Statistical Inference via Convex Optimization
Anatoli Juditsky and Arkadi Nemirovski · 2020
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