Senko I. Asymptotic properties of adjusted least squares estimator in vector linear model with errors-in-variables

Thesis deals with asymptotic properties of estimators in linear and polynomial errors-in-variables regressions. We consider functional vector linear error-in-variable regression, structural linear error-in-variable regression, and structural polynomial error-in-variable regression. For the functional vector linear error-in-variables regression with known covariance matrix of errors in regressors, conditions of consistency and strong consistency have been established for the adjusted least squares estimator of unknown matrix parameter, while heteroscedastic errors in response have bounded accuracy, decreasing accuracy, or dependent structure. For the homoscedastic case of functional vector linear error-in-variables model with known covariance matrix of errors in regressors, there are established conditions of asymptotic normality for the adjusted least squares estimator. These conditions exclude demand for the symmetry of the distribution of the multivariate error in independent variables. Also, we constructed a small sample modification for the adjusted least squares estimator, which preserves asymptotic properties, and which is more stable from small to moderate sample sizes. For the structural vector linear error-in-variables regression, we constructed estimators for the best mean square error individual and mean predictors. It is proved the strong consistency of such estimators. Confidence ellipsoid for the individual prediction is constructed. For the structural vector polynomial errors-in-variables, estimators for the best mean squared error individual and mean predictors are constructed, as well, with their strong consistency proved. Confidence interval for the individual predictor in quadratic model is constructed.