  We consider estimating the density of a response conditioning on an
error-prone covariate. Motivated by two existing kernel density estimators in
the absence of covariate measurement error, we propose a method to correct the
existing estimators for measurement error. Asymptotic properties of the
resultant estimators under different types of measurement error distributions
are derived. Moreover, we adjust bandwidths readily available from existing
bandwidth selection methods developed for error-free data to obtain bandwidths
for the new estimators. Extensive simulation studies are carried out to compare
the proposed estimators with naive estimators that ignore measurement error,
which also provide empirical evidence for the effectiveness of the proposed
bandwidth selection methods. A real-life data example is used to illustrate
implementation of these methods under practical scenarios. An R package, lpme,
is developed for implementing all considered methods, which we demonstrate via
an R code example in Appendix H.
