8 research outputs found
A Bayesian construction of asymptotically unbiased estimators
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 for a sample of size ).
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.Comment: 28 pages, 2 figure
Small Area Estimation under Square Root Transformed Fay-Herriot model with Functional Measurement Error in Covariates
We consider a small area estimation model under square-root transformation in
the presence of functional measurement error. When measurement error is
present, the Bayes predictor can no longer be used as it depends on the
covariates even if parameters are known. Therefore suitable replacements are
called for, and we propose a predictor that only depends on observed responses
and data obtained from a large secondary survey. Moreover, some estimating
methods of unknown parameters are considered. In the simulations section, We
evaluate the performance using the mean squared prediction error (MSPE) and
discuss several scenarios in terms of the number of areas and the sample size
in a large secondary survey.Comment: 12 pages, two table
立川市町丁目別住民意識調査分析追記—小地域推定モデル活用に向けて—
統計数理研究所75周年記念 –研究業績紹介