References
N. Chentsov, Estimation of the unknown density function,Dokl. Akad. Nauk SSSR,147, 45–48 (1962).
S. Yu. Efroimovich and M. S. Pinsker, The estimation of square-integrable spectral density from a sequence of observations.Probl. Inf. Transm.,17, 182–196 (1981).
S. Yu. Efroimovich and M. S. Pinsker, Estimation of square-integrable probability density of a random variable,Probl. Inf. Transm.,18, 19–38 (1982).
G. K. Golubev, LAN in the problems of nonparametric estimation of fuctions and lower bounds for quadratic risks,Theory Probab. Appl.,36, 152–157 (1991).
I. A. Ibragimov and R. Z. Khas'minskii.Statistical Estimation: Asymptotic Theory. Springer-Verlag, Berlin-New York (1981).
I. A. Ibragimov and R. Z. Khas'minskii, Asymptotically normal families of distributions and efficient estimation.Ann. Statist.,19, 1681–1724 (1991).
M. Radavičius, Efficient nonparametric estimation of distribution density in the basis of algebraic polynomials,Acta Appl. Math.,38, 13–35 (1995).
R. Rudzkis and M. Radavičius, Locally minimax efficiency of nonparametric estimates of square-integrable densities,Lith. Math. J.,33, 56–75 (1993).
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Institute of Mathematics and Informatics. Akademijos 4, 2600 Vilnius, Lithuania. Published in Lietuvos Matematikos Rinkinys, Vol. 37, No. 1, pp. 71–86, January–March, 1997.
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Radavičius, M. Lower bound for quadratic losses of estimation of infinite-dimensional parameter. Lith Math J 37, 54–65 (1997). https://doi.org/10.1007/BF02465440
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DOI: https://doi.org/10.1007/BF02465440