On integral functionals of a density

Elizbar Nadaraya and Grigol Sokhadze

Communications in Statistics - Theory and Methods, 2016, vol. 45, issue 23, 7086-7102

Abstract: Estimation 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.

Date: 2016
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DOI: 10.1080/03610926.2014.974825

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