Abstract: Residual-based analysis is generally considered a cornerstone of statistical methodology. For a special case of indirect regression, we investigate a 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 the 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.

Key words and phrases: Bandwidth selection, indirect regression estimator, inverse problems, regularization, residual-based empirical distribution function, smooth bootstrap.