A Statistical Version of Prophet Inequalities
نویسندگان
چکیده
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 would 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 Zi = Xi + Yi, where the Y ’s are any sequence of independent random variables. This research was supported by Grant no. 94-00186 from the United States Israel Binational Science Foundation (BSF) Jerusalem, Israel. Hebrew University, Department of Statistics University of Southern California, Department of Mathematics Hebrew University, Department of Statistics, and Center for Rationality and Interactive Decision Theory
منابع مشابه
Prophet Inequalities with Limited Information
In the classical prophet inequality, a gambler observes a sequence of stochastic rewards V1, ..., Vn and must decide, for each reward Vi, whether to keep it and stop the game or to forfeit the reward forever and reveal the next value Vi. The gambler’s goal is to obtain a constant fraction of the expected reward that the optimal offline algorithm would get. Recently, prophet inequalities have be...
متن کاملExpectation Inequalities Associated with Prophet Problems
Applications of the original prophet inequalities of Krengel and Sucheston are made to problems of order selection, non-measurable stop rules, look-ahead stop rUles, and iterated maps of random variables. Also, proofs are given of two results of Hill and Hordijk c?ncerning optimal orderings of uniform and exponential d~stributions. §l. INTRODUCTION Universal inequalities comparing the two func
متن کاملA Survey of Prophet Inequalities in Optimal Stopping Theory
The Illain purpose of this paper is to provide a brief survey of what has CODle to be known as "prophet inequalities" or ~~prophet problerns" in the t heory of optirnal stopping. rrhis survpy includes surnrnaries of the basic results, subs e quent extensioIls and variations of these results, Blain proof tools an d techniques (with concrete exarllples), a,ad a list of open problenls. Although t...
متن کاملAutomated Online Mechanism Design and Prophet Inequalities
Recent work on online auctions for digital goods has explored the role of optimal stopping theory — particularly secretary problems — in the design of approximately optimal online mechanisms. This work generally assumes that the size of the market (number of bidders) is known a priori, but that the mechanism designer has no knowledge of the distribution of bid values. However, in many real-worl...
متن کاملProphet Inequalities for Averages of Independent Non-Negative Random Variables
The main purpose of this paper is to prove the following theorem, which sharpens results of Krengel and Sucheston [11, 12] in which the weaker constant 2(1 +-(3) was obtained. (Here EX is the expected value of the ran dom variable X, and ~ and T are the sets of stop rules ~ n, and of a.s. finite stop rules, respectively.) Theorem 1.1. If Xl' ... , X n are independent non-negative random variab...
متن کامل