Modified Reweighted Fast and Consistent High Breakdown Estimator for High Dimensional Dataset

Outlier detection and classification algorithm play a critical role in statistical analysis. The reweighted fast and consistent high breakdown point (RFCH) estimator is an outlier resistant estimator of multivariate location and dispersion, but the application of the RFCH in high dimensional settings is hampered by some difficulties. One main difficulty is that the RFCH cannot be applied when the dimension exceeds the sample size. We proposed modifying RFCH (MRFCH) estimator to make it applicable in high dimensional settings. The basic idea of our proposed method is to modify the Mahalanobis distance so that it makes use of only the diagonal elements of the scatter matrix in the computation of the RFCH algorithm and hence tries to preserve the robustness properties of the RFCH estimator. As a result, we achieve a pretty robust and efficient high dimensional procedure for computing location and scatter matrix estimates and powerful outlier detection method. One of the main advantages of our proposed procedure over the existing RFCH is that it can be applied for both low and high dimensional datasets. Based on the real life datasets and simulation study, our proposed method showed promising results irrespective of sample size, dimensions, amount of contamination, computational time, and distance of the contamination. Thus, the proposed MRFCH algorithm can be applied to solve the problem of regression outliers in HDD and serve as a better alternative to the minimum regularized covariance determinant (MRCD) estimator