2nd special issue on robust analysis of complex data

Abstract

2nd special issue on robust analysis of complex data When we embarked to invite submissions for this 2nd special issue on robust analysis of complex data, we did so with the following call: Nowadays we are often confronted with large data sets in high dimensions. These new types of data have led to the emergence and use of complex models such as graphical models, models for complex correlation structures and models for functional data for instance. These complex structures pose many challenges. Specific ally, when many measurements on several variables are recorded, it becomes more likely that not all of these measurements are recorded with high accuracy. This may result in data of uneven quality that contains gross errors and other anomalies that need to be taken into account. Therefore, there is a need for robust procedures that can reliably analyze large data sets containing outliers and other data contamination. This special issue will focus mainly on computationally efficient, robust procedures to analyze such complex data sets. This call resulted in 37 submissions, from which five high quality papers have been selected for inclusion in this special issue. We greatly acknowledge the help of the CSDA co-editors to handle these papers and we thank all anonymous referees for their valuable comments, honest opinions and constructive suggestions. Dhaene and Zhu ( 2017) study the robustness properties of median-based estimators for the AR(1) coefficient in different types of additive outliers scenarios for panel data when the number of time-points is growing to infinity while the number of observed panels is fixed. They do so through showing that the influence function is bounded when outliers occur independently over time or are patched additive, i.e. they occur in random sequences of length k. Bali and Boente (2017) consider robust principal component estimation of several populations of functional data. They adapt methods from one population functional data, instead of estimating the covariance operator for each of the populations separately, Bali and Boente (2017) propose to use robust projection-pursuit estimators for the common directions under a common principal component model instead. The benefit is that considerably fewer parameters need to be estimated. A particular highlight of the article is that Bali and Boente (2017) extend the definition of a functional common principal component model to the situation in which the covariance operator does not exist or when the underlying distribution is not elliptical, and show how this still ensures Fisher-consistency. Chiancone et al. (2017) show how to robustify Sliced Inverse Regression (SIR), which has been shown in Cook (2007) to correspond to the maximum likelihood of an inverse regression model with Gaussian errors, by extending its inverse regression formulation to non-Gaussian errors with heavy tailed distributions. In contrast to alternative robust versions of SIR, Chiancone et al. (2017) do not replace the standard SIR estimators by robust versions bu...