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Computational algebraic methods in efficient estimation

Kobayashi, Kei and Wynn, Henry P. (2014) Computational algebraic methods in efficient estimation. In: Nielsen, Frank, (ed.) Geometric Theory of Information. Signals and communication technology. Springer, Cham, Switzerland, pp. 119-140. ISBN 978-319053165

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Identification Number: 10.1007/978-3-319-05317-2_6

Abstract

A strong link between information geometry and algebraic statistics is made by investigating statistical manifolds which are algebraic varieties. In particular it is 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 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 as homotopy continuation methods. Simple examples are given showing both equations and computations.

Item Type: Book Section
Official URL: http://www.springer.com/
Additional Information: © 2014 Springer International Publishing Switzerland
Subjects: Z Bibliography. Library Science. Information Resources > ZA Information resources > ZA4050 Electronic information resources
Z Bibliography. Library Science. Information Resources > ZA Information resources > ZA4450 Databases
Sets: Research centres and groups > Decision Support and Risk Group (DSRG)
Date Deposited: 12 Jan 2015 13:22
Last Modified: 12 Jan 2015 13:23
URI: http://eprints.lse.ac.uk/id/eprint/60728

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