Optimal Stopping for I.I.D. Random Variables Based on the Sequential Information of the Location of Relative Records Only

Abstract

Let X _j , j = 1,…, n be independent and identically distributed random variables. Like in the classical secretary problem, the optimal stopper only observes Y _j  = 1, if X _j is a (relative) record, and Y _j  = 0, otherwise. The actual X _j values are not revealed. The goal is to maximize the expected X value at which one stops. We show that the optimal number of observations one should skip before considering stopping depends heavily on the underlying distribution.

Keywords:

• Domain of attraction
• Relative rank
• Relative record
• Secretary problem
• Stopping rule
• Stopping value

Subject Classification:

• 60G40

ACKNOWLEDGMENT

This research was supported by the Israel Science Foundation Grant No. 467/04.

Notes

Recommended by N. Mukhopadhyay