Estimating optimal stopping rules in the multiple best choice problem with minimal summarized rank via the Cross-Entropy method

We consider the problem of maximizing the probability of choosing the largest from a sequence of N observations when N is a bounded random variable. The present paper gives a necessary and sufficient condition, based on the distribution of N, for the optimal stopping rule to have a particularly simple form: what Rasmussen and Robbins (1975) call an s(r) rule. A second result indicates that optimal stopping rules for this problem can, with one restriction, take virtually any form.

Download Full-text

Best-choice problems involving recall and uncertainty of selection when the number of observations is random

Advances in Applied Probability ◽

10.1017/s0001867800022370 ◽

1984 ◽

Vol 16 (01) ◽

pp. 111-130

Author(s):

Joseph D. Petruccelli

Keyword(s):

Optimal Stopping ◽

Random Variable ◽

Point Of View ◽

Stopping Rules ◽

Choice Problem ◽

Best Choice Problem ◽

Previous Formulation ◽

Optimal Stopping Rules ◽

Bounded Random Variable ◽

Selection Of

From one point of view this paper adds to a previous formulation of the best-choice problem (Petruccelli (1981)) the possibility that the number of available observations, rather than being known, is a bounded random variable N with known distribution. From another perspective, it expands the formulations of Presman and Sonin (1972) and Rasmussen and Robbins (1975) to include recall and uncertainty of selection of observations. The behaviour of optimal stopping rules is examined under various assumptions on the general model. For optimal stopping rules and their probabilities of best choice relations are obtained between the bounded and unbounded N cases. Two particular classes of stopping rules which generalize the s(r) rules of Rasmussen and Robbins (1975) are considered in detail.

Download Full-text

Best-choice problems involving recall and uncertainty of selection when the number of observations is random

Advances in Applied Probability ◽

10.2307/1427227 ◽

1984 ◽

Vol 16 (1) ◽

pp. 111-130 ◽

Cited By ~ 2

Author(s):

Joseph D. Petruccelli

Keyword(s):

Optimal Stopping ◽

Random Variable ◽

Point Of View ◽

Stopping Rules ◽

Choice Problem ◽

Best Choice Problem ◽

Previous Formulation ◽

Optimal Stopping Rules ◽

Bounded Random Variable ◽

Selection Of

From one point of view this paper adds to a previous formulation of the best-choice problem (Petruccelli (1981)) the possibility that the number of available observations, rather than being known, is a bounded random variable N with known distribution. From another perspective, it expands the formulations of Presman and Sonin (1972) and Rasmussen and Robbins (1975) to include recall and uncertainty of selection of observations. The behaviour of optimal stopping rules is examined under various assumptions on the general model. For optimal stopping rules and their probabilities of best choice relations are obtained between the bounded and unbounded N cases. Two particular classes of stopping rules which generalize the s(r) rules of Rasmussen and Robbins (1975) are considered in detail.

Download Full-text

On the best-choice problem when the number of observations is random

Journal of Applied Probability ◽

10.1017/s0021900200097035 ◽

1983 ◽

Vol 20 (01) ◽

pp. 165-171 ◽

Cited By ~ 5

Author(s):

Joseph D. Petruccelli

Keyword(s):

Optimal Stopping ◽

Random Variable ◽

Stopping Rules ◽

Necessary And Sufficient Condition ◽

Choice Problem ◽

Best Choice Problem ◽

Optimal Stopping Rule ◽

Optimal Stopping Rules ◽

Bounded Random Variable ◽

Necessary And Sufficient

We consider the problem of maximizing the probability of choosing the largest from a sequence of N observations when N is a bounded random variable. The present paper gives a necessary and sufficient condition, based on the distribution of N, for the optimal stopping rule to have a particularly simple form: what Rasmussen and Robbins (1975) call an s(r) rule. A second result indicates that optimal stopping rules for this problem can, with one restriction, take virtually any form.

Download Full-text