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 the n-observations through a test of ‘no-outlier hypothesis’ (TONH) to a weighted least-square regression estimation. The cluster phase partition the n-observations into h-set called main cluster and a minor cluster of size n?h. A robust distance emerge from the main cluster upon which a test of no outlier hypothesis’ is conducted. An initial WLS regression 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 the TONH to the Re-weighted regression estimation phase. Hence, we propose to call it cluster-based re-weighted regression (CBRR). The CBRR is compared with three existing procedures using two data sets known to exhibit masking and swamping. The performance of CBRR is further examined through simulation experiment. The results obtained from the data set illustration and the Monte Carlo study shows that the CBRR is effective in detecting multivariate outliers where other methods are susceptible to it. The CBRR does not require enormous computation and is substantially not susceptible to masking and swamping.     

An outlier-resistant test for heteroscedasticity in linear models

The presence of contamination often called outlier is a very common attribute in data. Among other causes, outliers in a homoscedastic model make the model heteroscedastic. Moreover, outliers distort diagnostic tools for heteroscedasticity such that it may not be correctly identified. In this article, we show how outliers affect heteroscedasticity diagnostics. We then proposed a robust procedure for detecting heteroscedasticity in the presence of outliers by robustifying the non-robust component of the Goldfeld–Quandt (GQ) test. The performance of the proposed procedure is examined using simulation experiment and real data sets. The proposed procedure offers great improvement where the conventional GQ and other procedures fail.