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Introduced by Kiefer and Wolfowitz \cite{KW56}, the nonparametric maximum likelihood estimator (NPMLE) is a widely used methodology for learning mixture odels and empirical Bayes estimation.
A. Dytso, S. Yagli, H. V. Poor, and S. Shamai (Shitz) · 1901
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Grenander functionals and Cauchy’s formula
Piet Groeneboom · 1902
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A generalization of the method of maximum likelihood: Estimating a mixing distribution (Abstract)
Herbert Robbins · 1950
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On the fluctuations of sums of random variables
Erik Sparre Andersen · 1954
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On the theory of mortality measurement. Part II
Ulf Grenander · 1956
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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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Convexity
H. G. Eggleston · 1958
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Nonparametric roughness penalties for probability densities
IJ Good and Ray A Gaskins · 1971
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On the number of zeros of general exponential polynomials
R. Tijdeman · 1971
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Maximum likelihood estimation of a compound poisson process
Léopold Simar · 1976
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Nonparametric maximum likelihood estimation of a mixing distribution
Nan Laird · 1978
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Abstract inference
Ulf Grenander · 1981
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Mixtures of exponential distributions
Nicholas P Jewell · 1982
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On the estimation of a probability density function by the maximum penalized likelihood method
Bernard W Silverman · 1982
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The geometry of mixture likelihoods: a general theory
Bruce G Lindsay · 1983
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The geometry of mixture likelihoods, part II: the exponential family
Bruce G Lindsay · 1983
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The Grenader estimator: A nonasymptotic approach
Lucien Birgé · 1989
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Information bounds and nonparametric maximum likelihood estimation
Piet Groeneboom and Jon A Wellner · 1992
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Consistent estimation of a mixing distribution
Brian G Leroux · 1992
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Isotonic estimators of monotone densities and distribution functions: basic facts
Piet Groeneboom and HP Lopuhaa · 1993
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Uniqueness of estimation and identifiability in mixture models
Bruce G Lindsay and Kathryn Roeder · 1993
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Mixture models: theory, geometry and applications
Bruce G Lindsay · 1995
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Rates of convergence for the Gaussian mixture sieve
C. R. Genovese and L. Wasserman · 2000
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A non asymptotic penalized criterion for gaussian mixture model selection
Cathy Maugis and Bertrand Michel · 2011
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Nonparametric estimation under shape constraints
Piet Groeneboom and Geurt Jongbloed · 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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Log-concavity and strong log-concavity: a review
Adrien Saumard and Jon A Wellner · 2014
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Global rates of convergence of the MLEs of log-concave and s s -concave densities
Charles R Doss and Jon A Wellner · 2016
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Consistent estimation of the order of mixture models
Christine Keribin · 2000
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Empirical Processes in M-Estimation
Sara van de Geer · 2000
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Entropies and rates of convergence for maximum likelihood and Bayes estimation for mixtures of normal densities
S. Ghosal and A.W. van der Vaart · 2001
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Posterior convergence rates of Dirichlet mixtures at smooth densities
Subhashis Ghosal and Aad van der Vaart · 2007
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Estimating a Polya frequency function 2
Jayanta Kumar Pal, Michael Woodroofe, and Mary Meyer · 2007
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Maximum likelihood estimation of a log-concave density and its distribution function: Basic properties and uniform consistency
Lutz Dümbgen and Kaspar Rufibach · 2009
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High-dimensional classification via nonparametric empirical bayes and maximum likelihood inference
Lee H Dicker and Sihai D Zhao · 2016
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Local maxima in the likelihood of Gaussian mixture models: Structural results and algorithmic consequences
Chi Jin, Yuchen Zhang, Sivaraman Balakrishnan, Martin J Wainwright, and Michael I Jordan · 2016
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Global rates of convergence in log-concave density estimation
Arlene KH Kim and Richard J Samworth · 2016
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Global empirical risk minimizers with ”shape constraints” are rate optimal in general dimensions
Qiyang Han · 2019
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Optimality of maximum likelihood for log-concave density estimation and bounded convex regression
Gil Kur, Yuval Dagan, and Alexander Rakhlin · 2019
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Comment: Minimalist g g -modeling
Roger Koenker and Jiaying Gu · 2019
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How many modes can a constrained Gaussian mixture have?
Navin Kashyap and Manjunath Krishnapur · 2020
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Yury Polyanskiy and Yihong Wu · 2020
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On the nonparametric maximum likelihood estimator for gaussian location mixture densities with application to gaussian denoising
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