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Teoriya Veroyatnostei i ee Primeneniya, 1981, Volume 26, Issue 1, Pages 15–31
(Mi tvp2448)
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This article is cited in 3 scientific papers (total in 3 papers)
On the correctness of statistical point estimation problem
N. N. Čencov Moscow
Abstract:
Strongly consistent (in the sense of convergence in variation) decision procedures $\Pi=\{\Pi_N\}$ for the statistical point estimation problem are considered. We prove that the statistical problem of estimation the probability distribution $P$ on $E=\{x\colon 0\le x\le 1\}$ by means of independent $P$-distributed bservations $x_i^*$ ($i=1,\dots,N$, $N\to\infty$) without additional a priori information about $P$ is incorrect in this sense. The unknown $P$ being a priori absolutely continuous, the problem turns out to be correct [15]. However this modified problem is found not to admit the uniformly consistent decision procedures. Also it does not admit the procedures with vanishing (at $N\to\infty$) supremum of the risk, when a loss function is given by a Kullback information deviation $I[P_N^*:P]$.
Received: 15.12.1979
Citation:
N. N. Čencov, “On the correctness of statistical point estimation problem”, Teor. Veroyatnost. i Primenen., 26:1 (1981), 15–31; Theory Probab. Appl., 26:1 (1981), 13–29
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https://www.mathnet.ru/eng/tvp2448 https://www.mathnet.ru/eng/tvp/v26/i1/p15
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Abstract page: | 227 | Full-text PDF : | 132 |
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