On some selection problem

Porosiński, Zdzisław; Szajowski, Krzysztof

doi:10.1007/bfb0008423

Cited by 5 publications

(3 citation statements)

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“…These sets are the same as in [16] (page 685). Using the same methodology we obtain the optimal strategy: it allows us to stop only in such a moment, when observed candidate is the largest so far and exceeds the value x .…”

Section: It Leads Tomentioning

confidence: 90%

“…In the Section 3 we consider full information duration problem (FIDP) in finite horizon with and without recall possibility. The duration problem is transformed to the optimal stopping problem for the Markov process similar to this applied by Bojdecki [2] and Prosiński and Szajowski [16] (see Section 3.1). In Section 3.2 we present results related to the best-choice duration problem (BCDP) with and without recall possibility.…”

Section: Duration Problems For the Full-information Casementioning

confidence: 99%

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Duration problem: basic concept and some extensions

2016

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Abstract. We consider a sequence of independent random variables with the known distribution observed sequentially. The observation n is assumed to be a value of one order statistics such as s : n-th, where 1 s n. It the instances following the nth observation it may remain of the s : m or it will be the value of the order statistics r : m (of m > n observations). Changing the rank of the observation, along with expanding a set of observations there is a random phenomenon that is difficult to predict. From practical reasons it is of great interest. Among others, we pose the question of the moment in which the observation appears and whose rank will not change significantly until the end of sampling of a certain size. We also attempt to answer which observation should be kept to have the "good quality observation" as long as possible. This last question was analysed by Ferguson, Hardwick and Tamaki (1991) in the abstract form which they called the problem of duration.This article gives a systematical presentation of the known duration models and a new modifications. We collect results from different papers on the duration of the extremal observation in the no-information (denoted as rank based) case and the full-information case. In the case of non-extremal observation duration models the most appealing are various settings related to the two extremal order statistics. In the no-information case it will be the maximizing duration of owning the relatively best or the second best object. The idea was formulated and the problem was solved by Szajowski and Tamaki (2006). The full-information duration problem with special requirement was presented by Kurushima and Ano (2010).

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Section: It Leads Tomentioning

confidence: 90%

Section: Duration Problems For the Full-information Casementioning

confidence: 99%

Duration problem: basic concept and some extensions

2016

Self Cite

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show abstract

“…Note that the sign of the functions F and G does not depend on the parameter α. These sets are the same as in [16] (page 685). Using the same methodology we obtain the optimal strategy: it allows us to stop only in such a moment, when observed candidate is the largest so far and exceeds the value x .…”

Section: Discussionmentioning

confidence: 99%

Duration problem: basic concept and some extensions

Porosiński,

Skarupski,

Szajowski

2016

Preprint

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We consider a sequence of independent random variables with the known distribution observed sequentially. The observation n is assumed to be a value of one order statistics such as s : n-th, where 1 s n. It the instances following the nth observation it may remain of the s : m or it will be the value of the order statistics r : m (of m > n observations). Changing the rank of the observation, along with expanding a set of observations there is a random phenomenon that is difficult to predict. From practical reasons it is of great interest. Among others, we pose the question of the moment in which the observation appears and whose rank will not change significantly until the end of sampling of a certain size. We also attempt to answer which observation should be kept to have the "good quality observation" as long as possible. This last question was analysed by Ferguson, Hardwick and Tamaki (1991) in the abstract form which they called the problem of duration.This article gives a systematical presentation of the known duration models and a new modifications. We collect results from different papers on the duration of the extremal observation in the no-information (denoted as rank based) case and the full-information case. In the case of non-extremal observation duration models the most appealing are various settings related to the two extremal order statistics. In the no-information case it will be the maximizing duration of owning the relatively best or the second best object. The idea was formulated and the problem was solved by Szajowski and Tamaki (2006). The full-information duration problem with special requirement was presented by Kurushima and Ano (2010).

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Full-Information Best Choice Problems with Imperfect Observation

Porosiński

1993

Operations Research ’92

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On some selection problem

Cited by 5 publications

References 2 publications

Duration problem: basic concept and some extensions

Duration problem: basic concept and some extensions

Duration problem: basic concept and some extensions

Full-Information Best Choice Problems with Imperfect Observation

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