Abstract: The defect of the existed methods for variance - covariance component estimation (VCE), including computational efficiency and statistical properties of Chi-square statistic, are analyzed and pointed out in this paper. The equivalent condition adjustment model is established from the generalized adjustment model by null-space operator, based on which the equivalent condition closure (ECC) and the formula of Chi-square statistic is derived. Moreover, the variance-covariance component model characterized with invertibility is constructed effectively and the analytical method used for VCE is proposed using ECC and invertible variance covariance component model (short for VCE-ECC method). Meantime, simplification formulas of VCE-ECC method are provided for four basic adjustment models correspondingly. Finally, results show there was no significant difference for estimated value of variance - covariance component between proposed method and existed VCE methods in the statistical significance, and the analytical method presented here could overcome the inherent defect in existed VCE methods.

Key words: Null-space operator, Equivalent condition closure, Invertible variance covariance component model, VCE-ECC method