Challenges of cellwise outliers

It is well-known that real data often contain outliers. The term outlier typically refers to a case, typically denoted by a row of the data matrix. In recent times a different type has come into focus, the cellwise outliers. These are suspicious cells (entries) that can occur anywhere in the data matrix. Even a relatively small proportion of outlying cells can contaminate over half the cases, which is a problem for robust methods. This article discusses the challenges posed by cellwise outliers, and some methods developed so far to deal with them. New results are obtained on cellwise breakdown values for location, covariance and regression. A cellwise robust method is proposed for correspondence analysis, with real data illustrations. The paper concludes by formulating some points for debate.