Consistency of elementwise-weighted total least squares estimator in a multivariate errors-in-variables model AX=B

摘要: A multivariate measurement error model AX≈B is considered. The errors in [A,B] are rowwise independent, but within each row the may be correlated. Some of columns observed without errors, and addition covariance matrices differ from to row. total structure supposed known up a scalar factor. fully weighted least squares estimator X studied, which case normal coincides with maximum likelihood estimator. We give mild conditions for weak strong consistency estimator, when number rows increases. results generalize Gallo given univariate homoscedastic (where B vector), extend Gleser model. derive objective function propose an iteratively reweighted numerical procedure.