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Some Information Theoretic Ideas Useful in Statistical Inference
Authors:Takis Papaioannou  Kosmas Ferentinos  Charalampos Tsairidis
Institution:(1) Department of Statistics and Insurance Science, University of Piraeus, 18534 Piraeus, Greece;(2) Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece;(3) Department of Social Administration, Democritus University of Thrace, 69100 Komotini, Greece
Abstract:In this paper we discuss four information theoretic ideas and present their implications to statistical inference: (1) Fisher information and divergence generating functions, (2) information optimum unbiased estimators, (3) information content of various statistics, (4) characterizations based on Fisher information. This paper was written while the first author was visiting the University of Cyprus, Department of Mathematics and Statistics.
Keywords:Information generating function  Information optimum estimation  Information content  Acid test properties  Quantal random censoring  Koziol–  Green model  Truncated data  Characterizations of Fisher information
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