Abstract
Consider a standard statistical hypothesis test, leading to a binary decision made by exploiting a certain dataset. Suppose that, later, part of the data is lost, and we want to refine the test by exploiting both the surviving data and the previous decision. What is the best one can do? Such a question, here referred to as the unlucky broker problem, can be addressed by very standard tools from detection theory, but the solution gives intriguing insights and is by no means obvious. We provide the general form of the optimal detectors and discuss in depth their modus operandi, ranging from simple likelihood ratio tests to more complex behaviors. Limiting cases, where either the surviving data or the initial decision is almost useless, are also discussed.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
