Article first published online: 1 FEB 2011
Copyright © 2011 John Wiley & Sons, Ltd.
Statistics in Medicine
Volume 30, Issue 14, pages 1722–1734, 30 June 2011
How to Cite
McIntyre, J. and Stefanski, L. A. (2011), Regression-assisted deconvolution. Statist. Med., 30: 1722–1734. doi: 10.1002/sim.4186
- Issue published online: 2 JUN 2011
- Article first published online: 1 FEB 2011
- Manuscript Accepted: 9 DEC 2010
- Manuscript Received: 13 NOV 2009
- density estimation;
- measurement error;
- mean–variance function model
We present a semi-parametric deconvolution estimator for the density function of a random variable biX that is measured with error, a common challenge in many epidemiological studies. Traditional deconvolution estimators rely only on assumptions about the distribution of X and the error in its measurement, and ignore information available in auxiliary variables. Our method assumes the availability of a covariate vector statistically related to X by a mean–variance function regression model, where regression errors are normally distributed and independent of the measurement errors. Simulations suggest that the estimator achieves a much lower integrated squared error than the observed-data kernel density estimator when models are correctly specified and the assumption of normal regression errors is met. We illustrate the method using anthropometric measurements of newborns to estimate the density function of newborn length. Copyright © 2011 John Wiley & Sons, Ltd.