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"Statistical Reports for Remote Agents" by Isaish Andrews and Jesse M. Shapiro
A statistician observes data informative about an unknown parameter and makes a report to an audience of agents who take a decision and suffer a loss. Agents may differ in their prior beliefs, information, or loss functions. We consider two notions of statistical risk for comparing reporting rules. The first, decision risk, evaluates the expected loss of an agent assuming the agent takes the decision prescribed by the report. The second, remote risk, evaluates the expected loss of an agent assuming the agent takes her optimal decision given the report. Rules that are appealing with respect to decision risk may be unappealing with respect to remote risk, and vice versa. For example, there is sometimes no rule that is admissible in both notions of risk, and hence no rule that minimizes weighted average risk with respect to full-support weights under both notions of risk. We obtain a more encouraging result for minimax optimality. Our results expose a possible tension in scientific research: rules that constitute good decisions (estimators) may not be good for conveying useful information to the audience, and vice versa.