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FIDUCIAL APPROACH FOR THE INVARIANT OPTIMAL STOPPING PROBLEM
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FIDUCIAL APPROACH FOR THE INVARIANT OPTIMAL STOPPING PROBLEM
Annotation
PII
S042473880000616-6-1
Publication type
Article
Status
Published
Authors
Vitaly Belenky  Aleksey Zaslavskiy
Edition
Volume 48 Issue 1
Pages
80-93
Abstract

This paper is the continuation of (Belenky, Zaslavsky, 2011). The optimal stopping problem for an invariant family is considered. New notion “fi ducial sequence” (FS) is defi ned. FS has an inusual dualistic property: its members have the same “physical dimension” that the observed sequence, but it is statistically equivalent to a “non-dimensional” relative sequence. This allows to formulate the problem of optimal stoping for invariant family with non-invariant criterion (that wasn’t possible earlier). Necessary formulas are given.

Keywords
invariant family, optimal stopping problem, fi ducial sequence, inertness principle
Date of publication
01.01.2012
Number of purchasers
1
Views
871
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References



Additional sources and materials

Belen'kij V.Z., Zaslavskij A.A. (2011): Osnovaniya teorii fidutsial'nykh veroyatnostej: printsip inertnosti // Ehkonomika i mat. metody. Vyp. 3.


Berezovskij B.A., Gnedin A.V. (1984): Zadacha nailuchshego vybora. M.: Nauka.


de Groot M. (1974): Optimal'nye statisticheskie resheniya. M.: Mir.


Dynkin E.B., Yushkevich A.A. (1967): Teoremy i zadachi o protsessakh Markova. M.: Nauka.


Zaks Sh. (1975): Teoriya statisticheskikh vyvodov. M.: Mir.


Leman Eh. (1979): Proverka statisticheskikh gipotez. M.: Nauka.


Gilbert J., Mosteller F. (1966): Recognizing the Maximum of a Sequence // J. American Statistic Association. Vol. 61. P. 35–73.


Moser L. (1956): On a problem of Cayley // Scripta mathematica. Vol. 24. P. 298–292.

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