Fiducial Generalized Inference In The Errors-in-variable Models

For the errors-in-variables models and the hybrid models,we propose two confi-dence intervals by fiducial generalized pivotal quantity and generalized fiducial distri-bution.Here are the main resultsWe discuss the large sample theory of the fiducial generalized confidence interval.and develop another way which guarantees that the fiducial generalized confidence intervals derived from the structural method maintain the asymptotic correct coverage probabilitiesFor the simple linear errors-in-variables models,we first analyse the Gleser-Hwang effect under three different identifiable assumptions.Then we construct confidence intervals for the parameters of interest by fiducial generalized pivotal quantity and generalized fiducial distribution.Thirdly,we generalized the above methods to the hybrid models.Finally,we compare our new approaches with other relative methods by Monte Carlo simulation.Results demonstrate that our new approaches performs better under various settingsFor the errors-in-variables model of the vector explanatory variable,we construct confidence interval for the parameter of interest by fiducial generalized pivotal quantity under two different identifiable assumptions.Then we compare our new approach with other relative methods by Monte Carlo simulation.Results demonstrate that our new approach performs better under certain settingsFinally,a summary of this thesis is presented and some interesting unsolved prob-lems are addressed.