{"ID":2839529,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.15373","arxiv_id":"2511.15373","title":"Consistent Empirical Bayes Estimation of the Mean of a Mixing Distribution with Applications to Treatment of Nonresponse","abstract":"We consider a Nonparametric Empirical Bayes (NPEB) framework. Let $Y_i$ be random variables, $Y_i \\sim f(y|θ_i)$, $i=1,...,n$, where $θ_i \\sim G$, and $θ_i \\in Θ$ are independent. The variables $Y_i $ are conditionally independent given $θ_i, \\; i=1,...,n$. The mixing distribution $G$ is unknown and assumed to belong to a nonparametric class $\\{G \\}$. Let $η(θ)$ be a function of $θ$. We address the problem of consistently estimating $E_G η(θ) \\equiv η_G$. This problem becomes particularly challenging when $G$ cannot be consistently estimated from the observed data. We motivate this problem, especially in contexts involving nonresponse and missing data. For such cases, a consistent estimation method is suggested and its performance is demonstrated through simulations.","short_abstract":"We consider a Nonparametric Empirical Bayes (NPEB) framework. Let $Y_i$ be random variables, $Y_i \\sim f(y|θ_i)$, $i=1,...,n$, where $θ_i \\sim G$, and $θ_i \\in Θ$ are independent. The variables $Y_i $ are conditionally independent given $θ_i, \\; i=1,...,n$. The mixing distribution $G$ is unknown and assumed to belong t...","url_abs":"https://arxiv.org/abs/2511.15373","url_pdf":"https://arxiv.org/pdf/2511.15373v1","authors":"[\"Eitan Greenshtein\"]","published":"2025-11-19T11:59:39Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}