Abstract
Inferential problems for Y-linked bisexual branching processes are studied. A parametric frequentist framework is considered, with the reproduction laws belonging to the power series family of distributions. This kind of model is appropriate for the analysis of the generation-by-generation evolution of the number of carriers of two alleles of a Y-linked gene in a two-sex monogamic population, assuming that females prefer males carrying one of the alleles. It is assumed that the only available data are the total number of females and the total number of males of each genotype in each generation. The estimation problem is tackled as an incomplete data problem. Maximum likelihood estimators for the main parameters of the model are derived using expectation-maximization method. Predictive distributions for as yet unobserved generations are derived, and the accuracy of the algorithm is illustrated by way of a simulated example.
Mathematics Subject Classification (2000): 60J80, 60J85, 62M05, 90D10, 92D25
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Acknowledgements
We thank the referee the comments and suggestions which have improved the paper. This research was supported by the Ministerio de Ciencia e Innovación and the FEDER through the Plan Nacional de Investigación Científica, Desarrollo e Innovación Tecnolóogica, grants MTM2006-08891 and MTM2009-13248.
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González, M., Gutiérrez, C., Martínez, R. (2010). Parametric inference for Y-linked gene branching models: Expectation-maximization method. In: González Velasco, M., Puerto, I., Martínez, R., Molina, M., Mota, M., Ramos, A. (eds) Workshop on Branching Processes and Their Applications. Lecture Notes in Statistics(), vol 197. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11156-3_14
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DOI: https://doi.org/10.1007/978-3-642-11156-3_14
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