A Statistical Version of Prophet Inequalities

David Assaf, Larry Goldstein & Ester Samuel-Cahn

All classical "prophet inequalities" for independent random variables hold also in the case where only a noise corrupted version of those variables is observable. That is, if the pairs (X1, Z1),...,(Xn,Zn) are independent with arbitrary, known joint distributions, and only the sequence Z1,...,Zn is observable, then all prophet inequalities which hold if the X's were directly observable still hold, even though the expected X-values (i.e. the payoffs) for both the and statistician, will be different. Our model includes, for example, the case when Zi=Xi+Yi, where the Y's are any sequence of independent random variables.

March, 1997
Published in: 
The Annals of Statistics 26 (1998), 1190-1197