The dramatic growth of big datasets presents a new challenge to data storage and analysis. Data reduction, or subsampling, that extracts useful information from is crucial step in big-data We propose an orthogonal subsampling (OSS) approach for with focus on linear regression models. inspired by the fact array two levels provides best experimental design models sense it minimizes average varian...

An efficient two-level model identification method aiming at maximising a model's generalisation capability is proposed for a large class of linear-in-the-parameters models from the observational data. A new elastic net orthogonal forward regression (ENOFR) algorithm is employed at the lower level to carry out simultaneous model selection and elastic net parameter estimation. The two regularisa...

Global depth, tangent depth and simplicial depths for classical and orthogonal regression are compared in examles and properies that are usefull for calculations are derived. Algorithms for the calculation of depths for orthogonal regression are proposed and tests for multiple regression are transfered to orthogonal regression. These tests are distribution free in the case of bivariate observat...