Regularization parameter selection in indirect regression by residual based bootstrap

Bissantz, N. and Chown, J. and Dette, H.

Volume: 30 Pages: 1255-1283
DOI: 10.5705/ss.202018.0160
Published: 2020

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. © 2020 Institute of Statistical Science. All rights reserved.

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