  Many practical problems are related to the pointwise estimation of dis-
tribution functions when data contains measurement errors. Motivation for these
problems comes from diverse fields such as astronomy, reliability, quality
control, public health and survey data. Recently, Dattner, Goldenshluger and
Juditsky (2011) showed that an estimator based on a direct inversion formula
for distribution functions has nice properties when the tail of the
characteristic function of the mea- surement error distribution decays
polynomially. In this paper we derive theoretical properties for this estimator
for the case where the error distri- bution is smoother and study its finite
sample behavior for different error distributions. Our method is data-driven in
the sense that we use only known information, namely, the error distribution
and the data. Applica- tion of the estimator to estimating hypertension
prevalence based on real data is also examined.
