**Julie McIntyre and Leonard A. Stefanski**

We present a semi-parametric deconvolution estimator for the density
function of a random variable *X* that is measured with
error. 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. Under common
parametric assumptions on the conditional mean and variance, the
estimator is root *n*-consistent for the true density of *X*, a
substantial improvement over the logarithmic rates achieved by
nonparametric deconvolution estimators. 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.

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