Confidence bands for multivariate and time dependent inverse regression models
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Date
2012-06-18
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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.
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Keywords
confidence bands, deconvolution, inverse problems, multivariate regression, nonparametric Regression, rates of convergence, time dependent regression function, uniform convergence