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Inverting Random Functions III: Discrete MLE Revisited
Mike A. Steel1 and Laszlo A. Szekely2
Biomathematics Research Centre, Mathematics and Statistics Department, University of Canterbury, Private Bag 4800, Christchurch 8041, New Zealand
Department of Mathematics, University of South Carolina, LeConte College, 1523 Greene Street, Columbia, SC 29208, USA
Annals of Combinatorics 13 (3) pp.365-382 September, 2009
AMS Subject Classification: 60C05, 62B10, 92B10, 94A17
This paper continues our earlier investigations into the inversion of random functions in a general (abstract) setting. In Section~\ref{two}, we investigate a concept of invertibility and the invertibility of the composition of random functions defined on finite sets. In Section~\ref{three}, we resolve some questions concerning the number of samples required to ensure the accuracy of maximum likelihood estimation (MLE) in the presence of `nuisance' parameters. A direct application to phylogeny reconstruction is given.
Keywords: random function, maximum likelihood estimation, phylogeny reconstruction


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