A common problem in the analysis of data from multi-environment trials is imbalance caused by missing observations. To get around this problem, different methods for imputing the missing values have been proposed based on the singular-value decomposition (SVD) of a matrix. However, this SVD can be affected by outliers and produce low quality imputations. In this talk, I will show four extensions of the methods that are resistant to outliers, replacing the standard SVD method with four robust SVD extensions. The evaluation of these methods is using exclusively numerical criteria in a simulation study and in a cross-validation study based on real data.
The robust SVD also can be used as a flexible tool to estimate the rank from a predictive point of view, it means, using cross-validation (CV) in contaminated matrices. Several statistical techniques for analyzing data matrices use lower rank approximations to these matrices, for which, in general, the appropriate rank must first be estimated depending on the objective of the study. The estimation can be conducted by cross-validation (CV), but most methods are not designed to cope with the presence of outliers, a very common problem in data matrices. The literature suggests one option to circumvent the problem, namely, the elimination of the outliers, but such information removal should only be performed when it is possible to verify that an outlier effectively corresponds to a collection or typing error. This conference presents a methodology that combines the robust singular value decomposition (rSVD) with a CV scheme, and this allows outliers to be taken into account without eliminating them. For this, three possible rSVD’s are considered and six resistant criteria are proposed for the choice of the rank, based on three classic statistics used in multivariate statistics. To test the performance of the various methods, a simulation study and an analysis of real data are described, using an exclusively numerical evaluation through Procrustes statistics and critical angles between subspaces of principal components.