MINQUE Method Variance Component Estimation for the Mixed Additive and Multiplicative Random Error Model

Abstract

To address the problem of inaccurate mixed additive and multiplicative random error stochastic model weighting, we apply the minimum norm quadratic unbiased estimator (MINQUE) to a mixed additive and multiplicative random error model (TMAMM). Then we construct the corresponding calculation formula and iterative algorithm. Based on the formula and algorithm, we estimate the corresponding additive error variance and multiplicative error variance components. The MINQUE variance component estimation (VCE) method is based on (1) invariance, (2) unbiasedness, and (3) minimum normality. Therefore, the variance component estimates derived from the MINQUE method for the mixed additive and multiplicative random error stochastic model also have unbiased and least norm properties. The mixed additive and multiplicative random error stochastic model is modified based on an estimated variance component valuation to obtain a more reasonable parameter valuation. Numerical simulation experiments, digital terrain model (DTM) experiments, and side net measurement are used to verify the effectiveness of the proposed method.