Empirical Bayes deconvolution estimates

Bradley Efron

Biometrika, 2016, vol. 103, issue 1, 1-20

Abstract: An unknown prior density $g(\theta )$ has yielded realizations $\Theta _1,\ldots ,\Theta _N$. They are unobservable, but each $\Theta _i$ produces an observable value $X_i$ according to a known probability mechanism, such as $X_i\sim {\rm Po}(\Theta _i)$. We wish to estimate $g(\theta )$ from the observed sample $X_1,\ldots ,X_N$. Traditional asymptotic calculations are discouraging, indicating very slow nonparametric rates of convergence. In this article we show that parametric exponential family modelling of $g(\theta )$ can give useful estimates in moderate-sized samples. We illustrate the approach with a variety of real and artificial examples. Covariate information can be incorporated into the deconvolution process, leading to a more detailed theory of generalized linear mixed models.

Date: 2016
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Citations: View citations in EconPapers (22)

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