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Activity Number: 474 - Nonparametric Density and Variance Estimation
Type: Contributed
Date/Time: Wednesday, August 2, 2017 : 8:30 AM to 10:20 AM
Sponsor: Section on Nonparametric Statistics
Abstract #322541 View Presentation
Title: Density Deconvolution Using the Phase Function with Unknown and Heterogeneous Measurement Errors
Author(s): Linh Hoang Nghiem* and Cornelis Potgieter
Companies: Southern Methodist University and Southern Methodist University
Keywords: deconvolution ; measurement errors ; density estimation ; phase function ; heterogeneity

The empirical phase function has recently been used as a tool for nonparametric density deconvolution when the true measurements are contaminated by additive random noise from an unknown distribution (Delaigle & Hall, 2016). This estimator assumes homogeneity of the measurement error. However, when all the measurement error components come from different symmetric distributions, the phase function is unaffected. This invariance property of the phase function can be employed in the setting where the measurement errors are heterogeneous. We propose a weighted empirical phase function (WEPF) where the weights adjust for heterogeneity. The properties of the WEPF estimator are considered. Simulation results show that this weighting can result in large decreases in MISE when estimating the phase function. Note that the estimation of the weights requires replicate observations for estimating the measurement error variance at the observation level. Finally, the construction of a deconvolution density estimator using WEPF is compared to the heterogeneous deconvolution estimator of Delaigle & Meister (2008). Our estimator proves to be competitive without knowledge of the error distribution.

Authors who are presenting talks have a * after their name.

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