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

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 those 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 with 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.