Regularization parameter selection in indirect regression by residual based bootstrap
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Date
2016
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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.
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Keywords
bandwidth selection, smooth bootstrap, residual-based empirical distribution function, regularization, indirect nonparametric regression, deconvolution function estimator