  Residual-based analysis is generally considered a cornerstone of statistical
methodology. For a special case of indirect regression, we investigate the
residual-based empirical distribution function and provide a uniform expansion
of this estimator, which is also shown to be asymptotically most precise. This
investigation naturally leads to a completely data-driven technique for
selecting a regularization parameter used in our indirect regression function
estimator. The resulting methodology is based on a smooth bootstrap of the
model residuals. A simulation study demonstrates the effectiveness of our
approach.
