E. Greenshtein

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20242026

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math.ST2026

Empirical Bayes Estimation of the Mean of a Function of the Latent Variable with Applications to the Treatment of Nonresponse

Eitan Greenshtein, Ya'acov Ritov

We consider the estimation of linear functionals of the mixing distribution in a nonparametric empirical Bayes framework. Our main interest is in situations in which the mixing dis…

math.ST2025

Consistent Empirical Bayes Estimation of the Mean of a Mixing Distribution with Applications to Treatment of Nonresponse

Eitan Greenshtein

We consider a Nonparametric Empirical Bayes (NPEB) framework. Let $Y_{i}$ be random variables, $Y_{i} \sim f (y ∣ I^¸_{i})$ , $i = 1, ..., n$ , where $I^¸_{i} \sim G$ , and $I^¸_{i} \in I^$ are independe…

math.ST2024

Consistent Empirical Bayes estimation of the mean of a mixing distribution without identifiability assumption. With applications to treatment of non-response

Eitan Greenshtein

{\bf Abstract} Consider a Non-Parametric Empirical Bayes (NPEB) setup. We observe $Y_{i}, \sim f (y ∣ I^¸_{i})$ , $I^¸_{i} \in I^$ independent, where $I^¸_{i} \sim G$ are independent $i = 1, ..., n$ .…