Abstract

Maximum likelihood estimation in statistics leads to the problem of maximizing a product of powers of polynomials. We study the algebraic degree of the critical equations of this optimization problem. This degree is related to the number of bounded regions in the corresponding arrangement of hypersurfaces, and to the Euler characteristic of the complexified complement. Under suitable hypotheses, the maximum likelihood degree equals the top Chern class of a sheaf of logarithmic differential forms. Exact formulae in terms of degrees and Newton polytopes are given for polynomials with generic coefficients.

pdf

Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 671-697
Launched on MUSE
2006-05-24
Open Access
No
Back To Top

This website uses cookies to ensure you get the best experience on our website. Without cookies your experience may not be seamless.