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Teor. Veroyatnost. i Primenen., 1967, Volume 12, Issue 1, Pages 39–50 (Mi tvp683)  

This article is cited in 2 scientific papers (total in 2 papers)

Incomplete Exponential Families and Unbiased Minimum Variance Estimates. I

A. M. Kagana, V. P. Palamodovb

a Leningrad
b Moscow

Abstract: Exponential family (9) of distributions on $R^1$ with polynomial relations (10) between the natural parameters $\vartheta_1,…,\vartheta_s$ is considered. The problem of unbiased estimation based on an independent sample of size $n\ge3$ from that population is investigated.
The main result of the paper foranulated as the basic theorem gives necessary and sufficient conditions for an arbitrary polynomial of sufficient statistics to be the best unbiased estimator of its expectation. This theorem solves one of the problems posed by Yu. V. Linnik in [3]. The original statistical problem is reduced (Lemma 2) to a differential-algebraic one by means of $D$-method due to Wijsman [7]. Some other results (Theorems 1 and 2) have an independent interest.

Full text: PDF file (800 kB)

English version:
Theory of Probability and its Applications, 1967, 12:1, 36–46

Bibliographic databases:

Received: 13.05.1966

Citation: A. M. Kagan, V. P. Palamodov, “Incomplete Exponential Families and Unbiased Minimum Variance Estimates. I”, Teor. Veroyatnost. i Primenen., 12:1 (1967), 39–50; Theory Probab. Appl., 12:1 (1967), 36–46

Citation in format AMSBIB
\Bibitem{KagPal67}
\by A.~M.~Kagan, V.~P.~Palamodov
\paper Incomplete Exponential Families and Unbiased Minimum Variance Estimates.~I
\jour Teor. Veroyatnost. i Primenen.
\yr 1967
\vol 12
\issue 1
\pages 39--50
\mathnet{http://mi.mathnet.ru/tvp683}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=216631}
\transl
\jour Theory Probab. Appl.
\yr 1967
\vol 12
\issue 1
\pages 36--46
\crossref{https://doi.org/10.1137/1112004}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Theory Probab. Appl., 50:3 (2006), 466–473  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Kagan A.M., Malinovsky Ya., “On the Nile Problem by Sir Ronald Fisher”, Electron. J. Stat., 7 (2013), 1968–1982  crossref  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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