{"ID":2892664,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.15077","arxiv_id":"2507.15077","title":"Unbiased estimation in one-parameter exponential families for the inverse of the natural parameter with extensions","abstract":"For one-parameter continuous exponential families, we identify an unbiased estimator of the inverse of the natural parameter $θ$ for cases where $θ\u003e 0$, extending an earlier result of \\cite{voinov1985unbiased} applicable to a normal model. We provide various applications for Gamma models, Inverse Gaussian models, distributions obtained by truncation, and ratios of normal means. Moreover, we extend the findings to estimating negative powers $θ^{-k}$, and more generally to complete monotone functions $q(θ)$.","short_abstract":"For one-parameter continuous exponential families, we identify an unbiased estimator of the inverse of the natural parameter $θ$ for cases where $θ\u003e 0$, extending an earlier result of \\cite{voinov1985unbiased} applicable to a normal model. We provide various applications for Gamma models, Inverse Gaussian models, distr...","url_abs":"https://arxiv.org/abs/2507.15077","url_pdf":"https://arxiv.org/pdf/2507.15077v2","authors":"[\"Pankaj Bhagwat\",\"Eric Marchand\"]","published":"2025-07-20T18:23:54Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}