A statistical version of prophet inequalities

• 成果类型: Article
• 署名作者: Assaf, D; Goldstein, L; Samuel-Cahn, E
• 署名单位: Hebrew University of Jerusalem; University of Southern California
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1998
• 页码: 1190-1197
• 关键词: independent random-variables

摘要

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)),..,(X-n,Z(n)) are independent with arbitrary, known joint distributions, and only the sequence Z(1),...,Z(n) 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 Z(i) = X-i + Y-i, where the Y's are any sequence of independent random variables.