Many kernel-based learning algorithms have the computational load scaled with the sample size n due to the column size of a full kernel Gram matrix K. This article considers the Nyström low-rank approximation. It uses a reduced kernel K̂, which is n×m, consisting of m columns (say columns...

The Gauss-Markov theorem provides a golden standard for constructing the best linear unbiased estimation for linear models. The main purpose of this article is to extend the Gauss-Markov theorem to include nonparametric mixed-effects models. The extended Gauss-Markov estimation (or prediction)...