Tsarehorodtsev Y. Asymptotic properties of estimators in linear and polynomial errors-in-variables model

In the thesis, the asymptotic properties of estimators in linear and polynomial measurement error models are considered. Structural linear scalar model, functional polynomial model and multidimensional functional regression model are studied. In a structural linear errors-in-variables model, a new parametrization is proposed in which expectation of the response appears in place of the intercept, which allows to allocate three groups of asymptotically independent estimators for the five regression parameters in the case of a given ratio of the error variances and two such groups if the error variance of the regressor is given. For a functional polynomial errors-in-variables model, sufficient conditions for the consistency of the adjusted least squares estimator of the regression parameters is obtained, as well as sufficient conditions for the asymptotic normality of the estimators. Vector linear errors-in-variables models are investigated. In the homoskedastic case, the total least squares estimators of the transition matrix is considered, and in the heteroskedastic case, the elementwise-weighted total least squares estimator is studied. Conditions for asymptotic normality of the estimators are obtained. In the homoskedastic case, a goodness-of-fit test is constructed, which works in the absence of intercept in the model, and the power of the test is investigated.