A Study on the Structural Equation Modeling using the Nearest Neighbor Variance Estimation

The strength of nearest neighbor variance estimation (NNVE) is its robustness against a large proportion of noise points and against deviation from normality of the signal. Consistent results with this method have been established. Under some reasonable assumptions, it has been shown that the covariance estimate is bounded and that each point has only bounded influence on the final estimates. NNVE outperformed the popular minimum volume ellipsoid (MVE) estimator in simulation studies, with a big improvement when the proportion of outliers was very large. In this study, outlier data is applied to the robust covariance. In the result, for outlier data, the strong performance of NNVE is demonstrated. Thus, we propose the robust SEM by using the NNVE method in the case of existing outliers.