A Bayesian construction of asymptotically unbiased estimators.
Year: 2020
Type: preprint
Abstract: A differential geometric framework to construct an asymptotically unbiased estimator of a function of a parameter is presented. The derived estimator asymptotically coincides with the uniformly minimum variance unbiased estimator, if a complete sufficient statistic exists. The framework is based on the maximum a posteriori estimation, where the prior is chosen such that the estimator is unbiased. The framework is demonstrated for the second-order asymptotic unbiasedness (unbiased up to $O(n^{-1})$ for a sample of size $n$). The condition of the asymptotic unbiasedness leads the choice of the prior such that the departure from a kind of harmonicity of the estimand is canceled out at each point of the model manifold. For a given estimand, the prior is given as an integral. On the other hand, for a given prior, we can address the bias of what estimator can be reduced by solving an elliptic partial differential equation. A family of invariant priors, which generalizes the Jeffreys prior, is mentioned as a specific example. Some illustrative examples of applications of the proposed framework are provided.
Source: arXiv (Cornell University)
Authors: Masayo Y. Hirose, Shuhei Mano
Institutions: Kyushu University, The Institute of Statistical Mathematics
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3135333159