Abstract:
For a general class of statistics Tn defined by a relation of the form
n∑i=1ψ(Xi,Tn)=0,
where Xi are observations, a number of results is proved which show that Tn (or, in some cases, their appropriate modifications T∗n) are locally asymptotically minimax estimates of the corresponding functional Φ(F) of the unknown distribution F provided the family of all admissible distributions F is sufficiently large.
Citation:
B. Ya. Levit, “On efficiency of a class of non-parametric estimates”, Teor. Veroyatnost. i Primenen., 20:4 (1975), 738–754; Theory Probab. Appl., 20:4 (1976), 723–740
\Bibitem{Lev75}
\by B.~Ya.~Levit
\paper On efficiency of a~class of non-parametric estimates
\jour Teor. Veroyatnost. i Primenen.
\yr 1975
\vol 20
\issue 4
\pages 738--754
\mathnet{http://mi.mathnet.ru/tvp3338}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=403052}
\zmath{https://zbmath.org/?q=an:0367.62041}
\transl
\jour Theory Probab. Appl.
\yr 1976
\vol 20
\issue 4
\pages 723--740
\crossref{https://doi.org/10.1137/1120081}
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