Estimating probability of occurrence of the most likely multinomial event |
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| Institution: | 1. Clinical Pharmacodynamics Program, Applied/Developmental Research Directorate, Leidos Biomedical Research, Inc, Frederick National Laboratory for Cancer Research, Frederick, MD;2. Division of Cancer Treatment and Diagnosis, National Cancer Institute, Bethesda, MD;1. Institute for Theoretical Biology, Humboldt-Universität zu Berlin, 10115, Berlin, Germany;2. Einstein Center for Neurosciences Berlin, Charitéplatz 1, 10117, Berlin, Germany;3. Bernstein Center for Computational Neuroscience, 10115, Berlin, Germany;1. Sorbonne Universités, UPMC Univ Paris 06, Laboratoire de Statistique Théorique et Appliquée (LSTA), France;2. Institut de Mathématiques de Bordeaux (UMR 5251), CNRS, Université de Bordeaux, France;3. Institut de Mathématiques de Toulouse (UMR 5219), CNRS, Université de Toulouse, France;4. Institut des Technologies Avancées du Vivant (USR 3505), CNRS, Toulouse, France |
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| Abstract: | The problem of estimating the parameters of a multinomial population arises in discrete multivariate analysis. This paper deals with the problem of estimating the probability associated with the most likely multinomial event. We consider several estimates, such as the maximum likelihood estimate and its modifications, and a Bayes estimate. Certain mathematical properties of the estimates are shown. Empirical results are given, showing the relative performance of the estimates with respect to the mean squared error as the loss function. |
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