Nonparametric confidence bands in deconvolution density estimation

Nicolai Bissantz, Lutz Dümbgen, Hajo Holzmann and Axel Munk

No 2007,03, Technical Reports from Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen

Abstract: Uniform confidence bands for densities f via nonparametric kernel estimates were first constructed by Bickel and Rosenblatt [Ann. Statist. 1, 1071.1095]. In this paper this is extended to confidence bands in the deconvolution problem g = f for an ordinary smooth error density . Under certain regularity conditions, we obtain asymptotic uniform confidence bands based on the asymptotic distribution of the maximal deviation (LÉ-distance) between a deconvolution kernel estimator . f and f. Further consistency of the simple nonparametric bootstrap is proved. For our theoretical developments the bias is simply corrected by choosing an undersmoothing bandwidth. For practical purposes we propose a new data-driven bandwidth selector based on heuristic arguments, which aims

Date: 2007
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