Abstract: The existing outlier detection methods in variance-covariance component estimation (VCE) are based on the residuals. However, the essential inputs of VCE are the second-order values of residuals and, thus it is more reasonable to carry out the outlier detection using these second-order values directly. In this paper, starting with the fundament VCE equations based on equivalent residuals with standard normal distribution, we propose a new method to detect the outliers of VCE inputs where the chi-square (χ2) and normal product (Np) statistics are used to test the residual squares and their products for one another with a given confidence probability, respectively. The results show that if a confidence probability α is used to detect outliers with normal distribution statistic in residual domain, it is equivalent to test the residual squares with the same confidence probability using χ2 statistic but to test the products of residuals with a confidence probability smaller than α. Therefore, the variance estimates are equivalent using residual based or χ2 based outlier detection, but the better covariance estimates are achievable using Np based outlier detection than residual based one.