Robust estimation and inference under cellwise and casewise contamination

Cellwise outliers are likely to occur together with casewise outliers in datasets of relatively large dimension. Recent work has shown that traditional high breakdown point procedures may fail when applied to such datasets. In this thesis, we consider this problem when the goal is to (1) estimate multivariate location and scatter matrix and (2) estimate regression coefficients and confidence intervals for inference, which both are cornerstones in multivariate data analysis. To address the first problem, we propose a two-step procedure to deal with casewise and cellwise outliers, which generally proceeds as follows: first, it uses a filter to identify cellwise outliers and replace them by missing values; then, it applies a robust estimator to the incomplete data to down-weight casewise outliers. We show that the two-step procedure is consistent under the central model provided the filter is appropriately chosen. The proposed two-step procedure for estimating location and scatter matrix is then applied in regression for the case of continuous covariates by simply adding a third step, which computes robust regression coefficients from the estimated robust multivariate location and scatter matrix obtained in the second step. We show that the three-step estimator is consistent and asymptotically normal at the central model, for the case of continuous covariates. Finally, the estimator is extended to handle both continuous and dummy covariates. Extensive simulation results and real data examples show that the proposed methods can handle both cellwise and casewise outliers similarly well.Science, Faculty ofStatistics, Department ofGraduat