## Statistical Science

### Comment: Minimalist $g$-Modeling

#### Abstract

Efron’s elegant approach to $g$-modeling for empirical Bayes problems is contrasted with an implementation of the Kiefer–Wolfowitz nonparametric maximum likelihood estimator for mixture models for several examples. The latter approach has the advantage that it is free of tuning parameters and consequently provides a relatively simple complementary method.

#### Article information

Source
Statist. Sci., Volume 34, Number 2 (2019), 209-213.

Dates
First available in Project Euclid: 19 July 2019

https://projecteuclid.org/euclid.ss/1563501634

Digital Object Identifier
doi:10.1214/19-STS706

Mathematical Reviews number (MathSciNet)
MR3983321

Zentralblatt MATH identifier
07110689

#### Citation

Koenker, Roger; Gu, Jiaying. Comment: Minimalist $g$-Modeling. Statist. Sci. 34 (2019), no. 2, 209--213. doi:10.1214/19-STS706. https://projecteuclid.org/euclid.ss/1563501634

#### References

• Andersen, E. D. (2010). The Mosek Optimization Tools Manual, Version 6.0. Available from: http://www.mosek.com.
• Deely, J. J. and Lindley, D. V. (1981). Bayes empirical Bayes. J. Amer. Statist. Assoc. 76 833–841.
• Efron, B. (2010). Large-Scale Inference: Empirical Bayes Methods for Estimation, Testing, and Prediction. Institute of Mathematical Statistics (IMS) Monographs 1. Cambridge Univ. Press, Cambridge.
• Efron, B. (2016). Empirical Bayes deconvolution estimates. Biometrika 103 1–20.
• Friberg, H. A. (2012). Users Guide to the R-to-Mosek Interface. Available at http://rmosek.r-forge.r-project.org.
• Heckman, J. and Singer, B. (1984). A method for minimizing the impact of distributional assumptions in econometric models for duration data. Econometrica 52 271–320.
• Jiang, W. and Zhang, C.-H. (2009). General maximum likelihood empirical Bayes estimation of normal means. Ann. Statist. 37 1647–1684.
• Kiefer, J. and Wolfowitz, J. (1956). Consistency of the maximum likelihood estimator in the presence of infinitely many incidental parameters. Ann. Math. Stat. 27 887–906.
• Koenker, R. and Gu, J. (2015). REBayes: An R Package for Empirical Bayes Methods. Available from https://cran.r-project.org/package=REBayes.
• Koenker, R. and Mizera, I. (2014). Convex optimization, shape constraints, compound decisions, and empirical Bayes rules. J. Amer. Statist. Assoc. 109 674–685.
• Laird, N. (1978). Nonparametric maximum likelihood estimation of a mixed distribution. J. Amer. Statist. Assoc. 73 805–811.
• Lindley, D. V. and Smith, A. (1995). A conversation with Dennis Lindley. Statist. Sci. 10 305–319.
• Neal, R. M. (2000). Markov chain sampling methods for Dirichlet process mixture models. J. Comput. Graph. Statist. 9 249–265.
• Robbins, H. (1950). A generalization of the method of maximum likelihood; estimating a mixing distribution (abstract). Ann. Math. Stat. 21 314–315.
• Ross, G. J. and Markwick, D. (2018). Dirichletprocess: An R Package for Fitting Complex Bayesian Nonparametric Models. Available at https://cran.r-project.org/web/packages/dirichletprocess/vignettes/dirichletprocess.pdf.
• Stefanski, L. and Carroll, R. J. (1990). Deconvoluting kernel density estimators. Statistics 21 169–184.