Abstract:
For a class of differentiable functions Φ(F) of distributions F, an analogue of the information matrix I(F) is considered. In terms of matrix I(F), bounds for risks in estimating Φ(F) are obtained; this is an extension, to the non-parametric case, of a result of J. Hajek [2]. Some examples are discussed including estimation of Φ(F) under the restriction that the values of differentiable functions Ψ(F) are known.
Citation:
Yu. A. Koševnik, B. Ya. Levit, “On a non-parametric analogue of the information matrix”, Teor. Veroyatnost. i Primenen., 21:4 (1976), 759–774; Theory Probab. Appl., 21:4 (1976), 738–753
\Bibitem{KosLev76}
\by Yu.~A.~Ko{\v s}evnik, B.~Ya.~Levit
\paper On a~non-parametric analogue of the information matrix
\jour Teor. Veroyatnost. i Primenen.
\yr 1976
\vol 21
\issue 4
\pages 759--774
\mathnet{http://mi.mathnet.ru/tvp3421}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=428578}
\zmath{https://zbmath.org/?q=an:0388.62037}
\transl
\jour Theory Probab. Appl.
\yr 1976
\vol 21
\issue 4
\pages 738--753
\crossref{https://doi.org/10.1137/1121087}
Linking options:
https://www.mathnet.ru/eng/tvp3421
https://www.mathnet.ru/eng/tvp/v21/i4/p759
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