Consistency Issues in Skew Random Fields: Investigating Proposed Alternatives and Identifying Persisting Problems

Multiple researchers have proposed skew random fields derived from multivariate skew distributions, yet the consistency of these fields has been questioned. Mahmoudian (2018) and Saber et al. (2018) have put forth alternative suggestions to address these concerns. In our study, we identify that the random fields outlined by Mahmoudian (2018) continue to demonstrate consistency issues, suggesting a flaw in their definition. Finally we propose a skew random field and apply it to spatial prediction.