Jack-knife technique for outlier detection and estimation of standard errors in PARAFAC models

In the last years, multi-way analysis has become increasingly important because it has proved to be a valuable tool, e.g. in interpreting data provided by instrumental methods that describe the multivariate and complex reality of a given problem. Parallel factor analysis (PARAFAC) is one of the most widely used multi-way models. Despite its usefulness in many applications, up to date there is no available tool in the literature to estimate the standard errors associated with the parameter estimates. In this study, we apply the so-called jack-knife technique to PARAFAC in order to find the associated standard errors to the parameter estimates from the PARAFAC model. The jack-knife technique is also shown to be useful for detecting outliers. An example of fluorescence data (emission/excitation landscapes) is used to show the applicability of the method.