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arXiv · 2507.15077

Unbiased estimation in one-parameter exponential families for the inverse of the natural parameter with extensions

Pankaj Bhagwat·Eric Marchand
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Abstract

For one-parameter continuous exponential families, we identify an unbiased estimator of the inverse of the natural parameter $\theta$ for cases where $\theta > 0$, 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 $\theta^{-k}$, and more generally to complete monotone functions $q(\theta)$.

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Pankaj Bhagwat, Eric Marchand. 2025-07-20. Unbiased estimation in one-parameter exponential families for the inverse of the natural parameter with extensions. https://arxiv.org/abs/2507.15077

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