Abstract:
This paper improves some results on the rate of decrease of minimax risk for nonparametric density estimators which have been proved in the previous work of the authors [2]. For example, we prove that infninff∗nsupf‖f−f∗n‖1>1 even if the density function f belongs to the class of entire functions of exponential type Λ (Λ is known).
Citation:
I. A. Ibragimov, R. Z. Khas'minskii, “More on the estimation of distribution densities”, Studies in mathematical statistics. Part V, Zap. Nauchn. Sem. LOMI, 108, "Nauka", Leningrad. Otdel., Leningrad, 1981, 72–88; J. Soviet Math., 25:3 (1984), 1155–1165
\Bibitem{IbrKha81}
\by I.~A.~Ibragimov, R.~Z.~Khas'minskii
\paper More on the estimation of distribution densities
\inbook Studies in mathematical statistics. Part~V
\serial Zap. Nauchn. Sem. LOMI
\yr 1981
\vol 108
\pages 72--88
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl3436}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=629401}
\zmath{https://zbmath.org/?q=an:0486.62039|0528.62032}
\transl
\jour J. Soviet Math.
\yr 1984
\vol 25
\issue 3
\pages 1155--1165
\crossref{https://doi.org/10.1007/BF01084794}
Linking options:
https://www.mathnet.ru/eng/znsl3436
https://www.mathnet.ru/eng/znsl/v108/p72
This publication is cited in the following 16 articles:
Juntong Chen, “Estimating a regression function in exponential families by model selection”, Bernoulli, 30:2 (2024)
Theory Probab. Appl., 69:3 (2024), 404–424
“Global rate optimality of integral curve estimators
in high order tensor models”, Theory Probab. Appl., 68:2 (2023), 250–266
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
Andriy Norets, Justinas Pelenis, “Adaptive Bayesian Estimation of Discrete‐Continuous Distributions Under Smoothness and Sparsity”, ECTA, 90:3 (2022), 1355
Andriy Norets, Justinas Pelenis, “Adaptive Bayesian estimation of conditional discrete-continuous distributions with an application to stock market trading activity”, Journal of Econometrics, 230:1 (2022), 62
Sébastien Da Veiga, Jean-Michel Loubes, Maikol Solís, “Efficient estimation of conditional covariance matrices for dimension reduction”, Communications in Statistics - Theory and Methods, 46:9 (2017), 4403
Rebelles G., “Pointwise Adaptive Estimation of a Multivariate Density Under Independence Hypothesis”, Bernoulli, 21:4 (2015), 1984–2023
Rebelles G., “l-P Adaptive Estimation of An Anisotropic Density Under Independence Hypothesis”, Electron. J. Stat., 9:1 (2015), 106–134
Goldenshluger A. Lepski O., “on Adaptive Minimax Density Estimation on R-D”, Probab. Theory Relat. Field, 159:3-4 (2014), 479–543
A. V. Gol'denshlyuger, O. V. Lepskiǐ, “General procedure for selecting linear estimators”, Theory Probab. Appl., 57:2 (2013), 209–226
Goldenshluger A., Lepski O., “Bandwidth Selection in Kernel Density Estimation: Oracle Inequalities and Adaptive Minimax Optimality”, Ann Statist, 39:3 (2011), 1608–1632
L. A. Sakhanenko, “Global rate optimality in a model for diffusion tensor imaging”, Theory Probab. Appl., 55:1 (2011), 77–90
Theory Probab. Appl., 52:1 (2008), 24–39
M. Hoffman, O. Lepski, “Random rates in anisotropic regression (with a discussion and a rejoinder by the authors)”, Ann. Statist., 30:2 (2002)
P.-L. Chow, R. Khasminskii, R. Liptser, “On estimation of time dependent spatial signal in Gaussian white noise”, Stochastic Processes and their Applications, 96:1 (2001), 161
Citation in format AMSBIB
Contact us: