Regularization parameter selection in indirect regression by residual based bootstrap

Abstract

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.

Keywords: bandwidth selection, indirect regression estimator, inverse problems, regularization, residual-based empirical distribution function, smooth bootstrap