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June 2003 Optimal confidence bands for shape-restricted curves
Lutz Dümbgen
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Bernoulli 9(3): 423-449 (June 2003). DOI: 10.3150/bj/1065444812

Abstract

Let $Y$ be a stochastic process on $[0,1]$ satisfying $\rm dY(t)=n^{1/2}f(t)\rm dt + \rm dW(t)$, where $n\ge 1$ 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.

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Lutz Dümbgen. "Optimal confidence bands for shape-restricted curves." Bernoulli 9 (3) 423 - 449, June 2003. https://doi.org/10.3150/bj/1065444812

Information

Published: June 2003
First available in Project Euclid: 6 October 2003

zbMATH: 1044.62051
MathSciNet: MR1997491
Digital Object Identifier: 10.3150/bj/1065444812

Rights: Copyright © 2003 Bernoulli Society for Mathematical Statistics and Probability

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Vol.9 • No. 3 • June 2003
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