Cluster-based multivariate outlier identification and re-weighted regression in linear models.

A cluster methodology, motivated by a robust similarity matrix is proposed for identifying likely multivariate outlier structure and to estimate weighted least-square (WLS) regression parameters in linear models. The proposed method is an agglomeration of procedures that begins from clustering then-observations through a test of ‘no-outlier hypothesis’ (TONH) to a weighted least-square regression estimation. The cluster phase partition then-observations intoh-set called main cluster and a minor cluster of sizen−h. A robust distance emerge from the main cluster upon which a test of no outlier hypothesis’ is conducted. An initialWLSregression estimation is computed from the robust distance obtained from the main cluster. Until convergence, a re-weighted least-squares (RLS) regression estimate is updated with weights based on the normalized residuals. The proposed procedure blends an agglomerative hierarchical cluster analysis of a complete linkage through theTONHto the Re-weighted regression estimation phase. Hence, we propose to call it cluster-based re-weighted regression (CBRR). TheCBRRis compared with three existing procedures using two data sets known to exhibit masking and swamping. The performance ofCBRRis further examined through simulation experiment. The results obtained from the data set illustration and the Monte Carlo study shows that theCBRRis effective in detecting multivariate outliers where other methods are susceptible to it. TheCBRRdoes not require enormous computation and is substantially not susceptible to masking and swamping. [ABSTRACT FROM AUTHOR]