Computational Algebraic Methods in Efficient Estimation

What is it about?

It is well known how to bias correct a standard Maximum Likelihood Estimator to make it "second order efficient". This paper covers models which can be defined algebraically, and we give a wide class of second order efficient estimators. The paper is unusual in that all the various quantities can be represented by polynomials. We can push this a long way, including using special, and recent, methods to solve the "estimating equations".

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Why is it important?

One of the first papers on the "algebraic statistics" and "information geometry" interface.