Abstract:
It is shown that in estimating the density p(x) by means of the statistics (1) the sequence τn=τ0n is optimal in the sense of the minimum integral mean squared error U2n(τn). An estimate ˆτn=ˆτn(X1,X2,…,Xn) for τ0n is constructed and a theorem is proved that gives conditions under which U2n(ˆτn)∼U2n(τ0n).
Citation:
È. A. Nadaraya, “On the integral mean squared error of some non-parametric estimates of the probability density”, Teor. Veroyatnost. i Primenen., 19:1 (1974), 131–139; Theory Probab. Appl., 19:1 (1974), 133–141
\Bibitem{Nad74}
\by \`E.~A.~Nadaraya
\paper On the integral mean squared error of some non-parametric estimates of the probability density
\jour Teor. Veroyatnost. i Primenen.
\yr 1974
\vol 19
\issue 1
\pages 131--139
\mathnet{http://mi.mathnet.ru/tvp2763}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=339393}
\zmath{https://zbmath.org/?q=an:0309.62025}
\transl
\jour Theory Probab. Appl.
\yr 1974
\vol 19
\issue 1
\pages 133--141
\crossref{https://doi.org/10.1137/1119010}
Linking options:
https://www.mathnet.ru/eng/tvp2763
https://www.mathnet.ru/eng/tvp/v19/i1/p131
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