Authors: Bissantz, Nicolai
Dette, Holger
Proksch, Katharina
Title: Confidence bands for multivariate and time dependent inverse regression models
Language (ISO): en
Abstract: Uniform asymptotic confidence bands for a multivariate regression function in an inverse regression model with a convolution-type operator are constructed. The results are derived using strong approximation methods and a limit theorem for the supremum of a stationary Gaussian field over an increasing system of sets. As a particular application asymptotic confidence bands for a time dependent regression function ft(x) (x 2 Rd; t 2 R) in a convolution-type inverse regression model are obtained. To the best knowledge of the authors the results presented in this paper are the first which provide uniform confidence bands for multivariate nonparametric function estimation in inverse problems.
Subject Headings: confidence bands
inverse problems
multivariate regression
nonparametric Regression
rates of convergence
time dependent regression function
uniform convergence
Issue Date: 2012-06-18
Appears in Collections:Sonderforschungsbereich (SFB) 823

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