Missing value imputation using least squares techniques in contaminated matrices

This paper describes strategies to reduce the possible effect of outliers on the quality of imputations produced by a method that uses a mixture of two least squares techniques: regression and lower rank approximation of a matrix. To avoid the influence of discrepant data and maintain the computational speed of the original scheme, pre-processing options were explored before applying the imputation method. The first proposal is to previously use a robust singular value decomposition, the second is to detect outliers and then treat the potential outliers as missing. To evaluate the proposed methods, a cross-validation study was carried out on ten complete matrices of real data from multi-environment trials. The imputations were compared with the original data using three statistics: a measure of goodness of fit, the squared cosine between matrices and the prediction error. The results show that the original method should be replaced by one of the options presented here because outliers can cause low quality imputations or convergence problems. • The imputation algorithm based on Gabriel's cross-validation method uses two least squares techniques that can be affected by the presence of outliers. The inclusion of a robust singular value decomposition allows both to robustify the procedure and to detect outliers and consider them later as missing. These forms of pre-processing ensure that the algorithm performs well on any dataset that has a matrix form with suspected contamination.