Dümbgen, Lutz (2003). Optimal Confidence Bands for Shape-Restricted Curves. Bernoulli, 9(3), pp. 423-449. International Statistical Institute 10.3150/bj/1065444812
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Let Y be a stochastic process on [0,1] satisfying dY(t)=n 1/2 f(t)dt+dW(t) , where n≥1 is a given scale parameter (`sample size'), W is standard Brownian motion and f is an unknown function. Utilizing suitable multiscale tests, we construct confidence bands for f with guaranteed given coverage probability, assuming that f is isotonic or convex. These confidence bands are computationally feasible and shown to be asymptotically sharp optimal in an appropriate sense.
Item Type: |
Journal Article (Original Article) |
|---|---|
Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science |
UniBE Contributor: |
Dümbgen, Lutz |
Subjects: |
500 Science > 510 Mathematics |
ISSN: |
1350-7265 |
Publisher: |
International Statistical Institute |
Language: |
English |
Submitter: |
Lutz Dümbgen |
Date Deposited: |
28 Jul 2015 11:55 |
Last Modified: |
05 Dec 2022 14:48 |
Publisher DOI: |
10.3150/bj/1065444812 |
BORIS DOI: |
10.7892/boris.70416 |
URI: |
https://boris.unibe.ch/id/eprint/70416 |
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