Agostini, Daniele Creator Faculty paolo.lella@polimi.it Alberelli, Davide Creator Grande, Francesco Creator Lella, Paolo Creator MATH / Applied Mathematics Illinois Institute of Technology Affiliated department Maximum likelihood Fermat hypersurface Likelihood correspondence 2015 2015-11-09 We study the critical points of the likelihood function over the Fermat hypersurface. This problem is related to one of the main problems in statistical optimization: maximum likelihood estimation. The number of critical points over a projective variety is a topological invariant of the variety and is called maximum likelihood degree. We provide closed formulas for the maximum likelihood degree of any Fermat curve in the projective plane and of Fermat hypersurfaces of degree 2 in any projective space. Algorithmic methods to compute the ML degree of a generic Fermat hypersurface are developed throughout the paper. Such algorithms heavily exploit the symmetries of the varieties we are considering. A computational comparison of the different methods and a list of the maximum likelihood degrees of several Fermat hypersurfaces are available in the last section. Article

born digital application/pdf en https://doi.org/10.18409/jas.v6i2.44 6.2 Open Access eng http://hdl.handle.net/10560/islandora:1007809