TY - GEN

T1 - Asymptotically efficient estimators for algebraic statistical manifolds

AU - Kobayashi, Kei

AU - Wynn, Henry P.

N1 - Funding Information:
This work was supported by JSPS KAKENHI Grant 24700288 and UK EPSRC Grant EP/H007377/1

PY - 2013

Y1 - 2013

N2 - 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 efficiency estimators can be constructed, such as bias corrected Maximum Likelihood Estimators and more general estimators, but for which the estimating equations are purely algebraic. In addition it is shown how Gröbner 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 are homotopy methods.

AB - 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 efficiency estimators can be constructed, such as bias corrected Maximum Likelihood Estimators and more general estimators, but for which the estimating equations are purely algebraic. In addition it is shown how Gröbner 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 are homotopy methods.

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U2 - 10.1007/978-3-642-40020-9_80

DO - 10.1007/978-3-642-40020-9_80

M3 - Conference contribution

AN - SCOPUS:84884915944

SN - 9783642400193

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 721

EP - 728

BT - Geometric Science of Information - First International Conference, GSI 2013, Proceedings

T2 - 1st International SEE Conference on Geometric Science of Information, GSI 2013

Y2 - 28 August 2013 through 30 August 2013

ER -