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Teor. Veroyatnost. i Primenen., 1995, Volume 40, Issue 4, Pages 934–938 (Mi tvp3760)  

Short Communications

Optimal unbiased estimators in additive models with bounded errors are deterministic

L. Mattnera, M. Reindersb

a Institut für Mathematische Stochastic, Universität Hamburg, Hambourg, Germany
b Universität Hannover, Institut für Mathematik, Hannover, Germany

Abstract: In an additive model $X=\vartheta+\varepsilon$, $\vartheta\in\Theta\subset{\mathbf R}^k$, let the errors $\varepsilon$ have a compactly supported but otherwise arbitrary known joint distribution. Let $g$ be a uniformly minimum variance unbiased estimator for its own expectation $\gamma(\vartheta)$. We show that under mild regularity conditions, $g$ is deterministic: for every $\vartheta\in\Theta$, $g(X)=\gamma(\vartheta)$ almost surely. Our proof uses a lemma on entire quotients of Fourier transforms which might be of independent interest.

Keywords: characteristic function, entire function, exponential type, Fourier transform, linear model, location parameter, shift model, uniformly minimum variance unbiased estimator.

Full text: PDF file (330 kB)

English version:
Theory of Probability and its Applications, 1995, 40:4, 772–777

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Received: 16.02.1993
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Citation: L. Mattner, M. Reinders, “Optimal unbiased estimators in additive models with bounded errors are deterministic”, Teor. Veroyatnost. i Primenen., 40:4 (1995), 934–938; Theory Probab. Appl., 40:4 (1995), 772–777

Citation in format AMSBIB
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\by L.~Mattner, M.~Reinders
\paper Optimal unbiased estimators in additive models with bounded errors are deterministic
\jour Teor. Veroyatnost. i Primenen.
\yr 1995
\vol 40
\issue 4
\pages 934--938
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1405163}
\zmath{https://zbmath.org/?q=an:0898.62027}
\transl
\jour Theory Probab. Appl.
\yr 1995
\vol 40
\issue 4
\pages 772--777
\crossref{https://doi.org/10.1137/1140090}
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