The Maximum Likelihood Degree
代数几何
2007-06-13 v1 统计理论
统计理论
摘要
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.
引用
@article{arxiv.math/0406533,
title = {The Maximum Likelihood Degree},
author = {Fabrizio Catanese and Serkan Hosten and Amit Khetan and Bernd Sturmfels},
journal= {arXiv preprint arXiv:math/0406533},
year = {2007}
}
备注
32 pages, latex