Maximum likelihood degree of Fermat hypersurfaces via Euler characteristics

Wang, Botong

doi:10.1090/proc/13127

Maximum likelihood degree of Fermat hypersurfaces via Euler characteristics
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by Botong Wang PDF

Proc. Amer. Math. Soc. 144 (2016), 3649-3655 Request permission

Abstract:

Maximum likelihood degree of a projective variety is the number of critical points of a general likelihood function. In this note, we compute the maximum likelihood degree of Fermat hypersurfaces. We give a formula of the maximum likelihood degree in terms of the constants $\beta _{\mu , \nu }$, which is defined to be the number of complex solutions to the system of equations $z_1^\nu =z_2^\nu =\cdots =z_\mu ^\nu =1$ and $z_1+\cdots +z_\mu +1=0$.

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