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  Bump detection in heterogeneous Gaussian regression.

Enikeeva, F., Munk, A., & Werner, F. (2018). Bump detection in heterogeneous Gaussian regression. Bernoulli, 24(2), 1266-1306. doi:10.3150/16-BEJ899.

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Item Permalink: http://hdl.handle.net/21.11116/0000-0000-BA6C-6 Version Permalink: http://hdl.handle.net/21.11116/0000-0003-4F3D-2
Genre: Journal Article

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2555326.pdf (Publisher version), 712KB
 
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https://projecteuclid.org/euclid.bj/1505980896 (Publisher version)
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 Creators:
Enikeeva, F., Author
Munk, A.1, Author              
Werner, F.1, Author              
Affiliations:
1Research Group of Statistical Inverse-Problems in Biophysics, MPI for Biophysical Chemistry, Max Planck Society, ou_1113580              

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Free keywords: Change point detection; Heterogeneous Gaussian regression; Minimax testing theory
 Abstract: We analyze the effect of a heterogeneous variance on bump detection in a Gaussian regression model. To this end, we allow for a simultaneous bump in the variance and specify its impact on the difficulty to detect the null signal against a single bump with known signal strength. This is done by calculating lower and upper bounds, both based on the likelihood ratio. Lower and upper bounds together lead to explicit characterizations of the detection boundary in several subregimes depending on the asymptotic behavior of the bump heights in mean and variance. In particular, we explicitly identify those regimes, where the additional information about a simultaneous bump in variance eases the detection problem for the signal. This effect is made explicit in the constant and/or the rate, appearing in the detection boundary. We also discuss the case of an unknown bump height and provide an adaptive test and some upper bounds in that case.

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Language(s): eng - English
 Dates: 2017-09-212018-05
 Publication Status: Published in print
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 Table of Contents: -
 Rev. Method: Peer
 Identifiers: DOI: 10.3150/16-BEJ899
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Title: Bernoulli
Source Genre: Journal
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Pages: - Volume / Issue: 24 (2) Sequence Number: - Start / End Page: 1266 - 1306 Identifier: -