Kernel density estimation with Berkson error

Given a sample {Xi}i=1n from fX we construct kernel density estimators for fY, the convolution of fX with a known error density fε. This problem is known as density estimation with Berkson error and has applications in epidemiology and astronomy. Little is understood about bandwidth selection for Berkson density estimation. We compare three approaches to selecting the bandwidth both asymptotically, using large-sample approximations to the MISE, and at finite samples, using simulations. Our results highlight the relationship between the structure of the error fε and the optimal bandwidth. In particular the results demonstrate the importance of smoothing when the error term fε is concentrated near 0. We propose a data-driven bandwidth estimator and test its performance on NO2 exposure data.