## The Annals of Statistics

### A statistical version of prophet inequalities

#### Abstract

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 $(X_1, Z_1),\ldots,(X_n, Z_n)$ are independent with arbitrary, known joint distributions, and only the sequence $Z_1 ,\ldots,Z_n$ is observable, then all prophet inequalities which would 1 n hold if the $X$’s were directly observable still hold, even though the expected $X$-values (i.e., the payoffs) for both the prophet and statistician, will be different. Our model includes, for example, the case when $Z_i=X_i + Y_i$, where the $Y$’s are any sequence of independent random variables.

#### Article information

Source
Ann. Statist., Volume 26, Number 3 (1998), 1190-1197.

Dates
First available in Project Euclid: 21 June 2002

https://projecteuclid.org/euclid.aos/1024691094

Digital Object Identifier
doi:10.1214/aos/1024691094

Mathematical Reviews number (MathSciNet)
MR1635385

Zentralblatt MATH identifier
0929.62088

#### Citation

Assaf, David; Goldstein, Larry; Samuel-Cahn, Ester. A statistical version of prophet inequalities. Ann. Statist. 26 (1998), no. 3, 1190--1197. doi:10.1214/aos/1024691094. https://projecteuclid.org/euclid.aos/1024691094

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