Optimal Stopping for I.I.D. Random Variables Based on the Sequential Information of the Location of Relative Records Only
Ester Samuel‐Cahn · Sequential Analysis · 2007
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.