Comparison of robust regression methods in the presence of cellwise and casewise outliers

Until the 2000s, the preprocessing stage of data analysis focused on casewise (rowwise) outliers in a data matrix where rows are observations and columns are variables. Since the early 2000s, cellwise outliers have been introduced, where each cell in the data matrix is considered as a potential outlier. Such outliers are likely to appear in datasets together with casewise outliers. Cellwise outliers are relatively likely to occur in datasets along with rowwise outliers. Estimation of the location and dispersion matrix, which are the cornerstones of multivariate data analysis, and estimation of regression coefficients for inference are of great importance at this point. In this paper, imputation methods used in multivariate data sets in the presence of cellwise and row outliers by detecting cellwise and row outliers under THCM and ICM models are compared with robust statistical methods that will be less affected by these observations. In recent studies on data analysis, in order to make maximum use of the uncontaminated part of the data, it is preferred to detect outliers on a cell-by-cell basis rather than on a case-by-case basis. Moreover, algorithms are proposed to utilize substitution methods and/or robust estimators for parameter estimation after cellwise outlier detection. In this study, firstly, the concept of outliers and the types of situational and cellwise outliers are discussed and the mechanisms of these outliers are analyzed. Then, the methods of identifying these two types of outliers and the performances of robust estimators used in parameter estimation after identification in regression analysis are examined and compared on Automobile dataset and simulation study.