This thesis proposes different robust methods in an attempt to keep using the idea of PWR and LP\iVR even beyond the usual assumptions of such outliers, independent or correlated non Gaussian noises and random missing data. Therefore,
this thesis is divided into three parts. The first part introduces five different robust methodologies to extend the validity of PWR and LPWR to describe data contaminated with outliers and independent noises. The second part pays special exception when the noise structure is correlated.