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| 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 | |
| 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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