ISSN: 2222-6990
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The existing procedures for structural equation modelling involve in goodness of fit test for the sample covariance matrix by the structural model can no longer work in high dimensional datasets. The sample covariance can easily be influenced by outlier’s presence in the datasets. This affect the estimation of the sample mean and sample covariance not being accurate and as well cause inefficiency in the computation. Therefore, there is need to suggest a robust covariance estimator the L_1-median with Weiszfeld algorithm that will resolve the outliers problem in high dimensional dataset. This test is subjected to conditions of sample size (n), variables (p) percentages of outliers (?) with ?=0.05. Simulation study carried out and the results show that when variable is minor both test performed but the new robust covariance test is better. At both middle and greater variables the existing test cannot compute the rate when p>n cases. Generally, the results shows that the newly incorporated robust covariance test performed better compare to the existing test.
Arrigoni, F., Rossi, B., Fragneto, P., & Fusiello, A. (2018). Robust synchronization in SO (3) and SE (3) via low-rank and sparse matrix decomposition. Computer Vision and Image Understanding.
Bollen, K. A., Kirby, J. B., Curran, P. J., Paxton, P. M., & Chen, F. (2007). Latent variable
Models under misspecification: two-stage least squares (2SLS) and maximum likelihood (ML) estimators. Sociological Methods & Research, 36(1), 48-86.
Bianco, A., & Boente, G. (2002). On the asymptotic behavior of one-step estimates in
Heteroscedastic regression models. Statistics & probability letters, 60(1), 33-47.
Campbell, N. A. (1980). Robust procedures in multivariate analysis I: Robust covariance
Estimation. Applied statistics, 231-237.
Cardot, H. and Godichon-Baggioni, A. (2017). Fast Estimation of the Median Covariation
Matrix with Application to Online Robust Principal Component7s Analysis. TEST, 26, 461-480.
Davies, P. L. (1987). Asymptotic Behaviour of $ S $-Estimates of Multivariate Location
Parameters and Dispersion Matrices. The Annals of Statistics, 15(3), 1269-1292.
Huber, P. J. (1964). Robust estimation of a location parameter. The annals of mathematical
Statistics, 35(1), 73-101.
Maronna, R. A., Stahel, W. A., & Yohai, V. J. (1992). Bias-robust estimators of multivariate
Scatter based on projections. Journal of Multivariate Analysis, 42(1), 141-161.
Rousseeuw, P. J., & Driessen, K. V. (1999). A fast algorithm for the minimum covariance
Determinant estimator. Technometrics, 41(3), 212-223.
Rousseeuw, P. J. (1984). Least median of squares regression. Journal of the American statistical
Association, 79(388), 871-880.
Rousseeuw, P. J. (1985). Multivariate estimation with high breakdown point. Mathematical
Statistics and applications, 8(283-297), 37.
Tang, P., & Phillips, J. M. (2016). The robustness of estimator composition. In Advances in Neural Information Processing Systems (pp. 929-937).
Pison, G., Van Aelst, S., & Willems, G. (2003). Small sample corrections for LTS and MCD.
In Developments in Robust Statistics (pp. 330-343). Physica, Heidelberg.
Peña, D., & Prieto, F. J. (2001). Multivariate outlier detection and robust covariance matrix
Estimation. Technometrics, 43(3), 286-310.
Vardi, Y. and Zhang, C.-H. (2000). The multivariate L1-median and associated data depth.
Proc. Natl. Acad. Sci. USA, 97(4):1423-1426.
In-Text Citation: (Ahmed, Kasim, & Zulkifli, 2018)
To Cite this Article: Ahmed, H., Kasim, M. M., & Zulkifli, M. (2018). Robust Weiszfeld’s Structural Equation Modelling in Covariance Matrices. International Journal of Academic Research in Business and Social Sciences, 8(12), 1773–1784.
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