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The Robbins estimator is the most iconic and widely used procedure in the empirical Bayes literature for the Poisson model.
Asymptotically subminimax solutions of compound statistical decision problems
Robbins, H. (1951) · 1951
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Estimation by the minimum distance method
Wolfowitz, J. (1953) · 1953
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Estimation by the minimum distance method in nonparametric stochastic difference equations
Wolfowitz, J. (1954) · 1954
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Maximum likelihood and minimum χ 2 \chi^{2} estimates of the logistic function
Berkson, J. (1955) · 1955
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Consistency of the maximum likelihood estimator in the presence of infinitely many incidental parameters
Kiefer, J. and Wolfowitz, J. (1956) · 1956
Earlier work this paper cites.
An Empirical Bayes Approach to Statistics
Robbins, H. (1956) · 1956
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The minimum distance method
Wolfowitz, J. (1957) · 1957
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Smooth empirical Bayes estimation for one-parameter discrete distributions
Maritz, J. (1966) · 1966
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Information-type measures of difference of probability distributions and indirect observations
Csiszár, I. (1967) · 1967
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Construction of sequences estimating the mixing distribution
Deely, J. and Kruse, R. (1968) · 1968
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On the smooth empirical Bayes approach to testing of hypotheses and the compound decision problem
Maritz, J. (1968) · 1968
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An empirical Bayes smoothing technique
Lemon, G. H. and Krutchkoff, R. G. (1969) · 1969
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Empirical bayes estimation for the Poisson distribution
Maritz, J. (1969) · 1969
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The sequential generation of d d -optimum experimental designs
Wynn, H. P. (1970) · 1970
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A continuous empirical Bayes smoothing technique
Bennett, G. K. and Martz, H. (1972) · 1972
Earlier work this paper cites.
Theory of optimal experiments
Fedorov, V. V. (1972) · 1972
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Maximum likelihood estimation of a compound Poisson process
Simar, L. (1976) · 1976
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Minimum Hellinger distance estimates for parametric models
Beran, R. (1977) · 1977
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Convergence in distribution of minimum-distance estimators
Bolthausen, E. (1977) · 1977
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The minimum distance method of testing
Pollard, D. (1980) · 1980
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Mixtures of exponential distributions
Jewell, N. P. (1982) · 1982
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Empirical Bayes estimates using the nonparametric maximum likelihood estimate for the prior
Laird, N. M. (1982) · 1982
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Monotone empirical Bayes estimators for the continuous one-parameter exponential family
Houwelingen, J. v. and Stijnen, T. (1983) · 1983
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Parametric empirical Bayes inference: theory and applications
Morris, C. N. (1983) · 1983
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A method for minimizing the impact of distributional assumptions in econometric models for duration data
Heckman, J. and Singer, B. (1984) · 1984
Cited alongside, same era.
Asymptotic properties of maximum likelihood estimates in the mixed Poisson model
Lambert, D. and Tierney, L. (1984) · 1984
Cited alongside, same era.
A general approach to the optimality of minimum distance estimators
Millar, P. (1984) · 1984
Cited alongside, same era.
Complete class theorems for estimation of multivariate poisson means and related problems
Brown, L. and Farrell, R. (1985) · 1985
Cited alongside, same era.
An introduction to empirical Bayes data analysis
Casella, G. (1985) · 1985
Comparison of empirical Bayes and full Bayes approaches for before–after road safety evaluations
Persaud, B., Lan, B., Lyon, C., and Bhim, R. (2010) · 2010
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Statistical inference: the minimum distance approach
Basu, A., Shioya, H., and Park, C. (2011) · 2011
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The poisson compound decision problem revisited
Brown, L. D., Greenshtein, E., and Ritov, Y. (2013) · 2013
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Two modeling strategies for empirical Bayes estimation
Efron, B. (2014) · 2014
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Minimax bounds for estimation of Normal mixtures
Kim, A. K. (2014) · 2014
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Convex optimization, shape constraints, compound decisions, and empirical Bayes rules
Koenker, R. and Mizera, I. (2014) · 2014
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Cited alongside, same era.
Admissible estimation, dirichlet principles and recurrence of birth-death chains on ℤ + p \mathbb{Z}_{+}^{p}
Johnstone, I. (1986) · 1986
Cited alongside, same era.
Estimation of the mixing distribution for a normal mean with applications to the compound decision problem
Edelman, D. (1988) · 1988
Cited alongside, same era.
Consistency of maximum likelihood estimators for certain nonparametric families, in particular: mixtures
Pfanzagl, J. (1988) · 1988
Cited alongside, same era.
Efficiency versus robustness: the case for minimum hellinger distance and related methods
Lindsay, B. G. (1994) · 1994
Cited alongside, same era.
Optimal rate of convergence for finite mixture models
Chen, J. (1995) · 1995
Cited alongside, same era.
Mixture models: theory, geometry and applications
Lindsay, B. G. (1995) · 1995
Cited alongside, same era.
Near-optimal-sample estimators for spherical gaussian mixtures
Suresh, A. T., Orlitsky, A., Acharya, J., and Jafarpour, A. (2014) · 2014
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Consistency of the MLE under mixture models
Chen, J. (2017) · 2017
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Rebayes: an r package for empirical bayes mixture methods
Koenker, R. and Gu, J. (2017) · 2017
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On the structure of the least favorable prior distributions
Dytso, A., Poor, H. V., Bustin, R., and Shamai, S. (2018) · 2018
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Strong identifiability and optimal minimax rates for finite mixture estimation
Heinrich, P. and Kahn, J. (2018) · 2018
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Shape constrained density estimation via penalized rényi divergence
Koenker, R. and Mizera, I. (2018) · 2018
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Empirical Bayes methods
Maritz, J. S. and Lwin, T. (2018) · 2018
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A characterization of all single-integral, non-kernel divergence estimators
Jana, S. and Basu, A. (2019) · 2019
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On the non-asymptotic and sharp lower tail bounds of random variables
Zhang, A. R. and Zhou, Y. (2020) · 2020
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Empirical Bayes: Concepts and Methods
Efron, B. (2021) · 2021
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Computer Age Statistical Inference, Student Edition: Algorithms, Evidence, and Data Science
Efron, B. and Hastie, T. (2021) · 2021
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Miao, Z., Kong, W., Vinayak, R. K., Sun, W., and Han, F. (2021) · 2021
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Sharp regret bounds for empirical Bayes and compound decision problems
Polyanskiy, Y. and Wu, Y. (2021) · 2021
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A nonparametric regression alternative to empirical bayes approaches to simultaneous estimation
Barbehenn, A. and Zhao, S. D. (2022) · 2022
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Characterizing the functional density power divergence class
Ray, S., Pal, S., Kar, S. K., and Basu, A. (2022) · 2022
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Empirical bayes via erm and rademacher complexities: the poisson model
Jana, S., Polyanskiy, Y., Teh, A. Z., and Wu, Y. (2023) · 2023
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