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The Method of Moments [Pea94] is one of the most widely used methods in statistics for parameter estimation, by means of solving the system of equations that match the population and estimated moments.
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Michel Krawtchouk · 1932
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James Victor Uspensky · 1937
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The problem of moments
James Alexander Shohat and Jacob David Tamarkin · 1943
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Consistency of the maximum likelihood estimator in the presence of infinitely many incidental parameters
Jack Kiefer and Jacob Wolfowitz · 1956
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Theory of approximation of functions of a real variable
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The classical moment problem: and some related questions in analysis
N. I. Akhiezer · 1965
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Information Theory
Robert B. Ash · 1965
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Construction of sequences estimating the mixing distribution
JJ Deely and RL Kruse · 1968
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Calculation of Gauss quadrature rules
Gene H Golub and John H Welsch · 1969
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Scale mixtures of normal distributions
David F Andrews and Colin L Mallows · 1974
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Orthogonal polynomials
G. Szegö · 1975
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Maximum likelihood from incomplete data via the EM algorithm
Arthur P Dempster, Nan M Laird, and Donald B Rubin · 1977
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Nonparametric maximum likelihood estimation of a mixing distribution
Nan Laird · 1978
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Sub-Gaussian random variables
V. V Buldygin and Y. V. Kozachenko · 1980
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Properties of the maximum likelihood estimator of a mixing distribution
Bruce G Lindsay · 1981
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Large sample properties of generalized method of moments estimators
Lars Peter Hansen · 1982
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Mixtures of exponential distributions
Nicholas P Jewell · 1982
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Least squares quantization in pcm
Stuart Lloyd · 1982
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Natural exponential families with quadratic variance functions
Carl N Morris · 1982
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Mixture densities, maximum likelihood and the EM algorithm
Richard A Redner and Homer F Walker · 1984
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Asymptotic methods in statistical decision theory
L. Le Cam · 1986
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Application of the method of moments in probability and statistics
Persi Diaconis · 1987
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Estimation of the mixing distribution for a normal mean with applications to the compound decision problem
David Edelman · 1988
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Moment matrices: applications in mixtures
Bruce G Lindsay · 1989
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Recursiveness, positivity, and truncated moment problems
Raúl E Curto and Lawrence A Fialkow · 1991
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Optimal rate of convergence for finite mixture models
Jiahua Chen · 1995
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Mixture models: theory, geometry and applications
Bruce G Lindsay · 1995
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Semidefinite programming
Lieven Vandenberghe and Stephen Boyd · 1996
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On convergence properties of the EM algorithm for Gaussian mixtures
Lei Xu and Michael I Jordan · 1996
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The EM algorithm—an old folk-song sung to a fast new tune
Xiao-Li Meng and David Van Dyk · 1997
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Learning mixtures of Gaussians
Sanjoy Dasgupta · 1999
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Rates of convergence for the Gaussian mixture sieve
C. R. Genovese and L. Wasserman · 2000
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A cautionary note on likelihood ratio tests in mixture models
Wilfried Seidel, Karl Mosler, and Manfred Alker · 2000
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Efficiently learning mixtures of two Gaussians
Adam Tauman Kalai, Ankur Moitra, and Gregory Valiant · 2010
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Settling the polynomial learnability of mixtures of Gaussians
Ankur Moitra and Gregory Valiant · 2010
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The impact of constellation cardinality on Gaussian channel capacity
Yihong Wu and Sergio Verdú · 2010
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Algebraic Approximation: A Guide to Past and Current Solutions
Jorge Bustamante · 2011
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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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Matrix Analysis
Roger A. Horn and Charles R. Johnson · 2012
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Asymptotic statistics
Aad W. Van der Vaart · 2000
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Scale mixtures of Gaussians and the statistics of natural images
Martin J Wainwright and Eero P Simoncelli · 2000
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Learning mixtures of arbitrary Gaussians
Sanjeev Arora and Ravi Kannan · 2001
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Local operator theory, random matrices and Banach spaces
Kenneth R Davidson and Stanislaw J Szarek · 2001
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Entropies and rates of convergence for maximum likelihood and Bayes estimation for mixtures of normal densities
Subhashis Ghosal and Aad W van der Vaart · 2001
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Estimation of analytic functions
I Ibragimov · 2001
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Handbook of semidefinite programming: theory, algorithms, and applications
Henry Wolkowicz, Romesh Saigal, and Lieven Vandenberghe · 2012
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CVXOPT: A Python package for convex optimization
M Andersen, Joachim Dahl, and Lieven Vandenberghe · 2013
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Learning mixtures of spherical Gaussians: moment methods and spectral decompositions
Daniel Hsu and Sham M Kakade · 2013
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Convergence of latent mixing measures in finite and infinite mixture models
XuanLong Nguyen · 2013
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Tensor decompositions for learning latent variable models
Animashree Anandkumar, Rong Ge, Daniel Hsu, Sham M Kakade, and Matus Telgarsky · 2014
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Minimax bounds for estimation of normal mixtures
Arlene KH Kim · 2014
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Convex optimization, shape constraints, compound decisions, and empirical bayes rules
Roger Koenker and Ivan Mizera · 2014
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Tight bounds for learning a mixture of two gaussians
Moritz Hardt and Eric Price · 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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Algebraic identifiability of Gaussian mixtures
Carlos Améndola, Kristian Ranestad, and Bernd Sturmfels · 2016
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CVXPY: A Python-embedded modeling language for convex optimization
Steven Diamond and Stephen Boyd · 2016
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Bounds for the logarithm of the Euler gamma function and its derivatives
Harold G Diamond and Armin Straub · 2016
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Statistical and computational guarantees of Lloyd’s algorithm and its variants
Yu Lu and Harrison H Zhou · 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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Global analysis of expectation maximization for mixtures of two Gaussians
Ji Xu, Daniel J Hsu, and Arian Maleki · 2016
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Statistical guarantees for the em algorithm: From population to sample-based analysis
Sivaraman Balakrishnan, Martin J Wainwright, and Bin Yu · 2017
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Ten steps of EM suffice for mixtures of two Gaussians
Constantinos Daskalakis, Christos Tzamos, and Manolis Zampetakis · 2017
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Spectrum estimation from samples
Weihao Kong and Gregory Valiant · 2017
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Robust and proper learning for mixtures of Gaussians via systems of polynomial inequalities
Jerry Li and Ludwig Schmidt · 2017
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The moment problem
Konrad Schmüdgen · 2017
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Strong identifiability and optimal minimax rates for finite mixture estimation
Philippe Heinrich and Jonas Kahn · 2018
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Mixture models, robustness, and sum of squares proofs
Samuel B Hopkins and Jerry Li · 2018
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