The effects of error magnitude and bandwidth selection for deconvolution with unknown error distribution

Abstract

The error distribution is generally unknown in deconvolution problems with real applications. A separate independent experiment is thus often conducted to collect the additional noise data in these studies. In this paper, we study the nonparametric deconvolution estimation from a contaminated sample coupled with an additional noise sample. A ridge-based kernel deconvolution estimator is proposed and its asymptotic properties are investigated depending on the error magnitude. We then present a data-driven bandwidth selection algorithm by combining the bootstrap method and the idea of simulation extrapolation. The finite sample performance of the proposed methods and the effects of error magnitude are evaluated through simulation studies. A real data analysis for a gene Illumina BeadArray study is performed to illustrate the use of the proposed methods.

Keywords:

• deconvolution
• unknown error
• ridge-based approach
• bandwidth selection
• SIMEX

AMS Subject Classifications :

• 62G07
• 62G20

Acknowledgements

We are grateful to the Associate Editor and two reviewers for their valuable suggestions which substantially improved the paper. The research of XFW was supported in part by NIH UL1 RR024989. The research of D.Y. has been initiated and completed with the support of NSF-FRG DMS grants 0652571 and 0652684 (from University of Missouri, Columbia).