Robust Twoblock Simultaneous Dimension Reduction

TL;DR

This paper presents a new robust method for simultaneous dimension reduction in two data blocks, allowing individual model complexity tuning and outlier resistance, with applications to multivariate regression.

Contribution

It introduces the first statistically robust two-block dimension reduction method with both dense and sparse versions, enabling model and sparsity selection for each block.

Findings

Robust RTB methods resist various outliers.

RTB maintains efficiency across different dimensions.

Sparse RTB enables sparsity and complexity control in each block.

Abstract

This paper introduces robust twoblock (RTB) simultaneous dimension reduction, which is the first statistically robust method to perform simultaneous dimension reduction in two blocks of variables and allows to fine-tune the model complexity in each block individually. The paper proposes both a dense and a sparse version of the new method. Sparse RTB is the first robust estimator that allows to select both model complexity and the degree of sparsity for each block individually. RTB thereby allows to optimally extract and summarize the relevant portion of information in each block of data, also in the presence of outliers. As a corollary, the estimators can be recombined into a single estimate of regression coefficients for multivariate regression that is operable when the number of variables exceeds the number of cases in each block. An extensive simulation study illustrates that the new methods are resistant to different types of outliers, while maintaining estimation efficiency. across a range of dimensionality settings. These findings both hold true for the dense and the sparse method. The methods' performance is further illustrated on two example data sets and a straightforward algorithm is presented and made accessible in an open source repository.