Optimal Confidence Bands for Shape-Restricted Curves

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 Aug 2015 06:06

Publisher DOI:

10.3150/bj/1065444812

BORIS DOI:

10.7892/boris.70416

URI:

https://boris.unibe.ch/id/eprint/70416

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