Deconvolution density estimation with heteroscedastic errors using SIMEX

Details Deconvolution density estimation with heteroscedastic errors using SIMEX Deconvolution density estimation with heteroscedastic errors using SIMEX

2009-02-12

arxiv.org/abs/0902.2117v1

Mathematics

Statistics Theory

Submitted to the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics

Scientific paper

In many real applications, the distribution of measurement error could vary with each subject or even with each observation so the errors are heteroscedastic. In this paper, we propose a fast algorithm using a simulation-extrapolation (SIMEX) method to recover the unknown density in the case of heteroscedastic contamination. We show the consistency of the estimator and obtain its asymptotic variance and then address the practical selection of the smoothing parameter. We demonstrate that, through a finite sample simulation study, the proposed method performs better than the Fourier-type deconvolution method in terms of integrated squared error criterion. Finally, a real data application is conducted to illustrate the use of the method.

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