Abstract
This paper continues our earlier investigations into the inversion of random functions in a general (abstract) setting. In Section 2, we investigate a concept of invertibility and the invertibility of the composition of random functions defined on finite sets. In Section 3, 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.
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We thank the NZIMA Maclaurin Fellowship, the Phylogeny programme at the Isaac Newton Institute of Cambridge University, and Hungarian Bioinformatics MTKD-CT-2006-042794 for supporting this research. The second author was also supported in part by NSF DMS contracts 007 2187, 070 1111, and NIH NIGMS 1 R01 GM078991-01.
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Steel, M.A., Székely, L.A. Inverting Random Functions III: Discrete MLE Revisited. Ann. Comb. 13, 365–382 (2009). https://doi.org/10.1007/s00026-009-0023-z
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DOI: https://doi.org/10.1007/s00026-009-0023-z