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 dat...

Abstract A new Levenberg–Marquardt (LM) method for solving nonlinear least squares problems with convex constraints is described. Various versions of the LM have been proposed, their main differences being in choice a damping parameter. In this paper, we propose rule updating parameter so as to achieve both global and local convergence even under presence constraint set. The key our results per...

We study the problem of predicting as well best linear predictor in a bounded Euclidean ball with respect to squared loss. When only boundedness data generating distribution is assumed, we establish that least squares estimator constrained does not attain classical O(d?n) excess risk rate, where d dimension covariates and n number samples. In particular, construct such incurs an order ?(d3?2?n)...