Abstract
The average of a large number of random step functions produces a discontinuous surface with a large number of local optima although it may converge to a smooth surface with a unique optimum as the number of step functions tends to infinity. Such a function arises when certain types of econometric estimators are used, including variants of the maximum score estimator. I propose an algorithm for computing the optimum of such a surface, where standard gradient-based optimization methods are inapplicable. This algorithm replaces the discontinuous surface with a sequence of easily optimized continuous surfaces that converge to it. Sufficient conditions for the algorithm to converge to a global optimum are given and the algorithm's performance is evaluated in a simple but relevant application.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: 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.