Geodesic
Optimal unbiased estimators in additive models with bounded errors are deterministic
Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 4, pp. 934-938 Cet article a éte moissonné depuis la source Math-Net.Ru

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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, linear model, location parameter, shift model, uniformly minimum variance unbiased estimator.
Mots-clés : Fourier transform 
@article{TVP_1995_40_4_a23,
     author = {L. Mattner and M. Reinders},
     title = {Optimal unbiased estimators in additive models with bounded errors are deterministic},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {934--938},
     year = {1995},
     volume = {40},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_1995_40_4_a23/}
}
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L. Mattner; M. Reinders. Optimal unbiased estimators in additive models with bounded errors are deterministic. Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 4, pp. 934-938. http://geodesic.mathdoc.fr/item/TVP_1995_40_4_a23/