An information theoretic argument for the validity of the exponential model |
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Authors: | Konstantinos Zografos Kosmas Ferentinos |
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Institution: | (1) Section of Probability-Statistics and Operational Research, University of Ioannina, Department of Mathematics, 45110 Ioannina, Greece |
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Abstract: | Based on the Cramér-Rao inequality (in the multiparameter case) the lower bound of Fisher information matrix is achieved if and only if the underlying distribution is ther-parameter exponential family. This family and the lower bound of Fisher information matrix are characterized when some constraints in the form of expected values of some statistics are available. If we combine the previous results we can find the class of parametric functions and the corresponding UMVU estimators via Cramér-Rao inequality. |
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Keywords: | Fisher information Cramé r-Rao inequality UMVU estimators exponential family |
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