Polekha M. Estimation and goodness-of-fit test in a multivariate linear errors-in-variables models

The dissertation is devoted to constructing of consistent estimators of unknown matrix parameters in linear multivariate errors-in-variables models and to constructing of a goodness-of-fit test for such models. Based on the clustering idea, consistent estimators of unknown matrix parameter in explicit model and of the kernel of data matrix in implicit model are proposed. A goodness-of-fit test for a functional linear multivariate measurement error model is constructed. The proposed test uses an exponential weight function. A problem of constructing a goodness-of-fit test for a polynomial measurement error model is studied. But it is not natural to use an exponential weight function and, therefore, exponential moments. Instead in the thesis a polynomial weight function and power moments are used.