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Bayesian deconvolution: an R vinaigrette

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  • Roger Koenker

    (Institute for Fiscal Studies and UCL)

Abstract

Nonparametric maximum likelihood estimation of general mixture models pioneered by the work of Kiefer and Wolfowitz (1956) has been recently reformulated as an exponential family regression spline problem in Efron (2016). Both approaches yield a low dimensional estimate of the mixing distribution, g-modeling in the terminology of Efron. Some casual empiricism suggests that the Efron approach is preferable when the mixing distribution has a smooth density, while Kiefer-Wolfowitz is preferable for discrete mixing settings. In the classical Gaussian deconvolution problem both maximum likelihood methods appear to be preferable to (Fourier) kernel methods. Kernel smoothing of the Kiefer-Wolfowitz estimator appears to be competitive with the Efron procedure for smooth alternatives.

Suggested Citation

  • Roger Koenker, 2017. "Bayesian deconvolution: an R vinaigrette," CeMMAP working papers CWP38/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:38/17
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    References listed on IDEAS

    as
    1. Bradley Efron, 2016. "Empirical Bayes deconvolution estimates," Biometrika, Biometrika Trust, vol. 103(1), pages 1-20.
    2. Roger Koenker & Ivan Mizera, 2014. "Convex Optimization, Shape Constraints, Compound Decisions, and Empirical Bayes Rules," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 674-685, June.
    3. Koenker, Roger & Mizera, Ivan, 2014. "Convex Optimization in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 60(i05).
    Full references (including those not matched with items on IDEAS)

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