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  1. Mathematical Methods of Statistics
  2. Mathematical Methods of Statistics : Volume 19
  3. Mathematical Methods of Statistics : Volume 19, Issue 3, September 2010
  4. Minimax revisited. I
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Mathematical Methods of Statistics : Volume 26
Mathematical Methods of Statistics : Volume 25
Mathematical Methods of Statistics : Volume 24
Mathematical Methods of Statistics : Volume 23
Mathematical Methods of Statistics : Volume 22
Mathematical Methods of Statistics : Volume 21
Mathematical Methods of Statistics : Volume 20
Mathematical Methods of Statistics : Volume 19
Mathematical Methods of Statistics : Volume 19, Issue 4, December 2010
Mathematical Methods of Statistics : Volume 19, Issue 3, September 2010
Histogram selection for possibly censored data
Oracle convergence rate of posterior under projection prior and Bayesian model selection
Minimum distance estimation in normed linear spaces with Donsker-classes
A generalized skewness statistic for stationary ergodic martingale differences
Minimax revisited. I
Mathematical Methods of Statistics : Volume 19, Issue 2, June 2010
Mathematical Methods of Statistics : Volume 19, Issue 1, March 2010
Mathematical Methods of Statistics : Volume 18
Mathematical Methods of Statistics : Volume 17
Mathematical Methods of Statistics : Volume 16

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Minimax revisited. I

Content Provider Springer Nature Link
Author Levit, B.
Copyright Year 2010
Abstract In the problem of estimating bounded normal means, some improved lower bounds for the minimax quadratic risk are presented. Since these bounds hold for any sample size, not merely asymptotically, we refer to them as “nonasymptotic”.First, we will review and compare some well-known bounds due to van Trees, Chentsov, Bhattacharyya, Kooks, Casella-Strawderman, Ibragimov-Khasminskii, and Donoho. The goal is to obtain a reliable nonasymptotic lower bound for the minimax risk applicable to any sample sizes and — through the well-known method of the hardest one-dimensional subfamily — to related nonparametric estimation problems.A combined lower bound will be proposed and compared to the numerically evaluated minimax risk. This comparison shows that the proposed global bound is about 97% accurate for any sample sizes. The results will be applied to nonparametric estimation of linear functionals in the white Gaussian noise in Part II.
Starting Page 283
Ending Page 297
Page Count 15
File Format PDF
ISSN 10665307
Journal Mathematical Methods of Statistics
Volume Number 19
Issue Number 3
e-ISSN 19348045
Language English
Publisher Allerton Press, Inc.
Publisher Date 2010-10-03
Publisher Place Heidelberg
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword normal means minimax quadratic risk lower bounds nonasymptotic approach Minimax procedures Point estimation Estimation Nonparametric regression Statistical Theory and Methods
Content Type Text
Resource Type Article
Subject Statistics and Probability Statistics, Probability and Uncertainty
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