On integral functionals of a density |
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| Authors: | Elizbar Nadaraya |
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| Affiliation: | Faculty of Exact and Natural Sciences, Department of Mathematics, I. Javakhishvili Tbilisi State University, Tbilisi, Georgia |
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| Abstract: | ABSTRACTEstimation of a non linear integral functional of probability distribution density and its derivatives is studied. The truncated plug-in-estimator is taken for the estimation. The integrand function can be unlimited, but it cannot exceed polynomial growth. Consistency of the estimator is proved and the convergence order is established. Aversion of the central limit theorem is proved. As an example an extended Fisher information integral and generalized Shannon's entropy functional are considered. |
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| Keywords: | Central limit theorem Consistency Entropy Information Integral functional Plug-in-estimator. |
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