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 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 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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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
\Bibitem{MatRei95} \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 \mathnet{http://mi.mathnet.ru/tvp3760} \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} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1996WD22100020}