The Estimate of Variance Components Based on M-Estimate Residuals
Yue Ren-bin · Journal of Chongqing Jianzhu University · 2007
Based on the principle of the linear representation of the M-estimate,this paper derives the linear representation and nuisances of M-estimate for Heteroscedastic observations and the asymptotic variance-covariance matrix of the observations and the estimator of the unknown parameters;The unbiased estimate of the weighted quadric type of M-estimate residuals is derived from the asymptotic variance-covariance matrixes,it is the implicit function of heteroscedastic variances(or variance components) and nuisances.For the known error density,nuisances have their explicit representation only relative Heteroscedastic variances or their square roots,which constructs unbiased estimate form of heteroscedastic variance for computation.For Lp estimate and normal errors,the practical form estimating heteroscedastic variances is derived and applied in side-angle network.As compared with Helmert method,it shows that the estimate result of variance components and parameters varies significantly with p of Lp-estimate as gross errors occur;if there exist no gross errors or they are rejected right,there is a little gap in the estimate result.The estimate method derived in this paper can be used in adjustment of heteroscedastic model and for a good checkout of Helmert method.