The Goldenshluger–Lepski method for constrained least-squares estimators over RKHSs

We study an adaptive estimation procedure called the Goldenshluger–Lepski method in context of reproducing kernel Hilbert space (RKHS) regression. Adaptive provides a way selecting tuning parameters for statistical estimators using only available data. This allows us to perform without making strong assumptions about estimand. In contrast procedures such as training and validation, uses all data produce non-adaptive range values parameters. An estimator is selected by performing pairwise comparisons between these estimators. Applying non-trivial it requires simultaneous high-probability bound on comparisons. RKHS regression context, we choose our be clipped least-squares constrained lie ball RKHS. this made more complicated fact that cannot use L2 norm unknown. address two problems. first problem fixed, while second adapt over collection RKHSs.