Abstract
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.
This work was supported by JSPS KAKENHI Grant 24700288 and UK EPSRC Grant EP/H007377/1
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Kobayashi, K., Wynn, H.P. (2013). Asymptotically Efficient Estimators for Algebraic Statistical Manifolds. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2013. Lecture Notes in Computer Science, vol 8085. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40020-9_80
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DOI: https://doi.org/10.1007/978-3-642-40020-9_80
Publisher Name: Springer, Berlin, Heidelberg
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