Abstract:
We consider the asymptotic set-up of the following nonparametric problem. Choose the points of measurement X1,…,XN and estimate the unknown function f on the base of observations
Yi=f(Xi)+Gi(Xi,ω),i=1,…,N,
where noise variables G1,…,GN are independent when X1,…,XN are fixed. We suppose that the deviation of estimator from regression function f is measured in Lp metrix, 1⩽p<∞. The case p=∞ we consider in [1].
Citation:
I. A. Ibragimov, R. Z. Khas'minskii, “Asymptotic bounds on the quality of the nonparametric regression estimation in Lp”, Problems of the theory of probability distributions. Part VI, Zap. Nauchn. Sem. LOMI, 97, "Nauka", Leningrad. Otdel., Leningrad, 1980, 88–101; J. Soviet Math., 24:5 (1984), 540–550
\Bibitem{IbrKha80}
\by I.~A.~Ibragimov, R.~Z.~Khas'minskii
\paper Asymptotic bounds on the quality of the nonparametric regression estimation in~$\mathscr L_p$
\inbook Problems of the theory of probability distributions. Part~VI
\serial Zap. Nauchn. Sem. LOMI
\yr 1980
\vol 97
\pages 88--101
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl3267}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=602364}
\zmath{https://zbmath.org/?q=an:0457.62049|0551.62044}
\transl
\jour J. Soviet Math.
\yr 1984
\vol 24
\issue 5
\pages 540--550
\crossref{https://doi.org/10.1007/BF01702331}
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https://www.mathnet.ru/eng/znsl/v97/p88
This publication is cited in the following 3 articles:
A. A. Borovkov, Al. V. Bulinski, A. M. Vershik, D. Zaporozhets, A. S. Holevo, A. N. Shiryaev, “Ildar Abdullovich Ibragimov (on his ninetieth birthday)”, Russian Math. Surveys, 78:3 (2023), 573–583
I. A. Ibragimov, “Estimation of multivariate regression”, Theory Probab. Appl., 48:2 (2004), 256–272
R. Bentkus, “Rate of uniform convergence of statistical estimators of spectral density in spaces of differentiable functions”, Lith Math J, 25:3 (1986), 209
Citation in format AMSBIB
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