Abstract In the classical contamination models, such as gross-error (Huber and Tukey model or case-wise contamination), observations are considered units to be identified outliers not. This is very useful when number of variables moderately small. Alqallaf et al. (Ann Stat 37(1):311–331, 2009) show limits this approach for a larger introduced independent (cell-wise contamination) where now cell...

In this paper, we present the Anderson-Darling (AD) and Kolmogorov-Smirnov (KS) goodness of fit statistics for stationary and non-stationary random fields. Namely, we adopt an easy-to-apply method based on a random projection of a Hilbert-valued random field onto the real line R, and then, applying the well-known AD and KS goodness of fit tests. We conclude this paper by studying the behavior o...