We propose an estimator of prediction error using an approximate message passing (AMP) algorithm that can be applied to a broad range of sparse penalties. Following Stein’s lemma, the estimator of the generalized degrees of freedom, which is a key quantity for the construction of the estimator of the prediction error, is calculated at the AMP fixed point. The resulting form of the AMP-based est...

We introduce the weighted mixed almost unbiased ridge estimator (WMAURE) based on the weighted mixed estimator (WME) (Trenkler and Toutenburg 1990) and the almost unbiased ridge estimator (AURE) (Akdeniz and Erol 2003) in linear regression model. We discuss superiorities of the new estimator under the quadratic bias (QB) and the mean square error matrix (MSEM) criteria. Additionally, we give a ...

Estimators of the conditional expectation, i.e., prediction, function involve a global bias-variance trade off. In some cases, an estimator that yields unbiased estimates of the conditional expectation for a particular partitioning of the data may be desirable. Such estimators are calibrated with respect to the partitioning. We identify the conditional expectation given a particular partitionin...

Following the Gauss-Markov theorem the generalized lest-squares estimator is the best linear unbiased estimator but following the kriging theory its use is limited. This paper shows the kriging constraint on the classic generalized least-squares estimator.

this paper presents a discrete-time robust control for electrically driven robot manipulators in the task space. a novel discrete-time model-free control law is proposed by employing an adaptive fuzzy estimator for the compensation of the uncertainty including model uncertainty, external disturbances and discretization error. parameters of the fuzzy estimator are adapted to minimize the estimat...