Non-identifiable parametric probability models and reparametrization |
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Authors: | Abhijit Dasgupta Steven G Self Somesh Das Gupta |
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Institution: | 1. Division of Cancer Epidemiology and Genetics, National Cancer Institute, NIH, DHHS, USA;2. Fred Hutchinson Cancer Research Center, Seattle, WA, USA;3. Indian National Science Academy, New Delhi, India |
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Abstract: | Identifiability is a primary assumption in virtually all classical statistical theory. However, such an assumption may be violated in a variety of statistical models. We consider parametric models where the assumption of identifiability is violated, but otherwise satisfy standard assumptions. We propose an analytic method for constructing new parameters under which the model will be at least locally identifiable. This method is based on solving a system of linear partial differential equations involving the Fisher information matrix. Some consequences and valid inference procedures under non-identifiability have been discussed. The method of reparametrization is illustrated with an example. |
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Keywords: | Parametric identifiability Reparametrization Statistical inference Mixture model |
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