Authors: Birke, Melanie
Bissantz, Nicolai
Holzmann, Hajo
Title: Confidence bands for inverse regression models with application to gel electrophoresis
Language (ISO): en
Abstract: We construct uniform confidence bands for the regression function in inverse, homoscedastic regression models with convolution-type operators. Here, the convolution is between two non-periodic functions on the whole real line rather than between two period functions on a compact interval, since the former situation arguably arises more often in applications. First, following Bickel and Rosenblatt [Ann. Statist. 1, 1071–1095] we construct asymptotic confidence bands which are based on strong approximations and on a limit theorem for the supremum of a stationary Gaussian process. Further, we propose bootstrap confidence bands based on the residual bootstrap. A simulation study shows that the bootstrap confidence bands perform reasonably well for moderate sample sizes. Finally, we apply our method to data from a gel electrophoresis experiment with genetically engineered neuronal receptor subunits incubated with rat brain extract.
Subject Headings: Confidence band
Deconvolution
Inverse problem
Nonparametric regression
Rate of convergence
URI: http://hdl.handle.net/2003/25879
http://dx.doi.org/10.17877/DE290R-14439
Issue Date: 2008-11-26T14:50:14Z
Appears in Collections:Sonderforschungsbereich (SFB) 475

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