  The subject of this paper is the problem of nonparametric estimation of a
continuous distribution function from observations with measurement errors. We
study minimax complexity of this problem when unknown distribution has a
density belonging to the Sobolev class, and the error density is ordinary
smooth. We develop rate optimal estimators based on direct inversion of
empirical characteristic function. We also derive minimax affine estimators of
the distribution function which are given by an explicit convex optimization
problem. Adaptive versions of these estimators are proposed, and some numerical
results demonstrating good practical behavior of the developed procedures are
presented.
