Confidence bands for inverse regression models with application to gel electrophoresis

Melanie Birke, Nicolai Bissantz and Hajo Holzmann

No 2008,16, Technical Reports from Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen

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, 10711095] 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.

Keywords: Confidencebands; Inverseproblems; Deconvolution; Rates of convergences; Nonparametric Regression (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (1)

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