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Nonparametric maximum likelihood (NPML) for mixture models is a technique for estimating mixing distributions that has a long and rich history in statistics going back to the 1950s, and is closely related to empirical Bayes methods.
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Robbins, H. E., 1956. The empirical Bayes approach to statistical decision problems. In: Proc. Third Berkeley Symp. on Math. Statist. and Prob. Vol. 1. pp. 157–163
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Ghosal, S., van der Vaart, A. W., 2001. Entropies and rates of convergence for maximum likelihood and Bayes estimation for mixtures of normal densities. Ann. Stat. 29, 1233–1263
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McLachlan, G., Peel, D., 2004. Finite Mixture Models. John Wiley & Sons
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Brown, L. D., 2008. In-season prediction of batting averages: A field test of empirical Bayes and Bayes methodologies. Ann. Appl. Stat. 2, 113–152
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DasGupta, A., 2008. Asymptotic Theory of Statistics and Probability. Springer
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Hirsch, I. B., Abelseth, J., Bode, B. W., Fischer, J. S., Kaufman, F. R., Mastrototaro, J., Parkin, C. G., Wolpert, H. A., Buckingham, B. A., 2008. Sensor-augmented insulin pump therapy: Results of the first randomized treat-to-target study. Diabetes Technol. The. 10, 377–383
Mai, Q., Zou, H., Yuan, M., 2012. A direct approach to sparse discriminant analysis in ultra-high dimensions. Biometrika 99, 29–42
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Xie, X., Kou, S. C., Brown, L. D., 2012. SURE estimates for a heteroscedastic hierarchical model. J. Am. Stat. Assoc. 107, 1465–1479
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Dicker, L. H., Sun, T., Zhang, C.-H., Keenan, D. B., Shepp, L., 2013. Continuous blood glucose monitoring: A Bayes-hidden Markov approach. Stat. Sinica 23, 1595–1627
2013
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Donoho, D. L., Reeves, G., 2013. Achieving Bayes MMSE performance in the sparse signal + Gaussian white noise model when the noise level is unknown. In: IEEE Int. Symp. Inf. Theory. pp. 101–105
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Jaggi, M., 2013. Revisiting Frank-Wolfe: Projection-free sparse convex optimization. ICML 2013 28, 427–435
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Greenshtein, E., Park, J., 2009. Application of non parametric empirical Bayes estimation to high dimensional classification. J. Mach. Learn. Res. 10, 1687–1704
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Jiang, W., Zhang, C.-H., 2009. General maximum likelihood empirical Bayes estimation of normal means. Ann. Stat. 37, 1647–1684
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Efron, B., 2010. Large-Scale Inference: Empirical Bayes Methods for Estimation, Testing, and Prediction. Cambridge University Press
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Jiang, W., Zhang, C.-H., 2010. Empirical Bayes in-season prediction of baseball batting averages. In: Borrowing Strength: Theory Powering Applications – A Festschrift for Lawrence D. Brown. Institute of Mathematical Statistics, pp. 263–273
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MAQC Consortium, 2010. The microarray quality control (MAQC)-II study of common practices for the development and validation of microarray-based predictive models. Nat. Biotechnol. 28, 827–838
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Muralidharan, O., 2010. An empirical Bayes mixture method for effect size and false discovery rate estimation. Ann. Appl. Stat. 4, 422–438
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Gu, J., Koenker, R., 2017a. Empirical Bayesball remixed: Empirical Bayes methods for longitudinal data. J. Appl. Econom. 32 (3), 575–599
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Koenker, R., Mizera, I., 2014. Convex optimization, shape constraints, compound decisions, and empirical Bayes rules. J. Am. Stat. Assoc. 109, 674–685
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Wang, X., Wang, Y., 2015. Nonparametric multivariate density estimation using mixtures. Statistics and Computing 25 (2), 349–364
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Dicker, L. H., Zhao, S. D., 2016. High-dimensional classification via nonparametric empirical Bayes and maximum likelihood inference. Biometrika 103, 21–34
2016
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Gu, J., Koenker, R., 2016. On a problem of Robbins. Int. Stat. Rev. 84, 224–244
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Koenker, R., Gu, J., 2016. REBayes: An R package for empirical Bayes mixture methods
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