Robust design optimization using the price of robustness, robust least squares and regularization methods

Robust Methods for Partial Least Squares Regression

Partial Least Squares Regression (PLSR) is a linear regression technique developed to deal with high-dimensional regressors and one or several response variables. In this paper we introduce robustified versions of the SIMPLS algorithm being the leading PLSR algorithm because of its speed and efficiency. Because SIMPLS is based on the empirical cross-covariance matrix between the response variab...

Robust Estimation Using Least Trimmed Squares

A robust procedure is proposed, starting from least trimmed squares as the initial estimator. The asymptotic distribution of the two-step and multi-step estimators is derived. This allows the use with a pre-specified efficiency under normality. It is argued that the good performance, together with the simplicity of the procedure, should make this the robust estimator of choice for applied work.

Robust Least Squares and Applications

We consider least-squares problems where the coef-cient matrices A; b are unknown-but-bounded. We minimize the worst-case residual error using (convex) second-order cone programming (SOCP), yielding an algorithm with complexity similar to one singular value decomposition of A. The method can be interpreted as a Tikhonov regularization procedure, with the advantage that it provides an exact boun...

Level Robust Methods Based on the Least Squares Regression Estimator

Robust linear least squares regression

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