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- W1492515476 abstract "Let $x_1, cdots, x_n$ be a sample of size $n$ of an $operatorname{rv}$ with $operatorname{df} F(x - theta)$, where $F$ is known but $theta$ unknown. In this paper we make a Fourier approach to the problem of existence of a statistic $g(x_1, cdots, x_n)$ which is a uniformly minimum variance (UMV) estimator of its own mean value. We mention only some of the results. If $n = 1$ we find an NASC for an estimator $g(x_1)$ to be, in a restricted sense, UMV. This condition is given in terms of the zeroes of the ch.f. of $F$ and the support of the Fourier transform of $g$. If $n geqq 2$, it is shown that a statistic of the form $g(bar{x})$, where $bar{x}$ is the sample mean, cannot be UMV, unless $g$ is periodic or $F$ is a normal $operatorname{df}$. We prove the non-existence of a UMV-estimator of $theta$, provided that the tail of $F$ tends to zero rapidly enough. Finally, it is proved that no polynomial $P(x_1, cdots, x_n)$ can be a UMV-estimator, unless $F$ is a normal $operatorname{df}$." @default.
- W1492515476 created "2016-06-24" @default.
- W1492515476 creator A5056325791 @default.
- W1492515476 date "1975-05-01" @default.
- W1492515476 modified "2023-10-16" @default.
- W1492515476 title "Uniformly Minimum Variance Estimation in Location Parameter Families" @default.
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- W1492515476 doi "https://doi.org/10.1214/aos/1176343127" @default.
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