5 research outputs found
Computational algebraic methods in efficient estimation
A strong link between information geometry and algebraic statistics is made
by investigating statistical manifolds which are algebraic varieties. In
particular it it shown how first and second order efficient estimators can be
constructed, such as bias corrected Maximum Likelihood and more general
estimators, and for which the estimating equations are purely algebraic. In
addition it is shown how Gr\"obner basis technology, which is at the heart of
algebraic statistics, can be used to reduce the degrees of the terms in the
estimating equations. This points the way to the feasible use, to find the
estimators, of special methods for solving polynomial equations, such as
homotopy continuation methods. Simple examples are given showing both equations
and computations. *** The proof of Theorem 2 was corrected by the latest
version. Some minor errors were also corrected.Comment: 21 pages, 5 figure