Semiparametric A Function Of Model Parameter Estimation

This paper studies mainly the theories of the semiparametric errors-in-variables modelwhere(x, t) is fixed in R^p×R¹. The errors e andδare independent as well as their elements with E[(e,δ')'] = 0, Cov[(e,δ')'] =σ²I_p+1 where 0 <σ² <∞is unknown parameter,βis a p×1 unknown vector of parameters, and g(·) is unknown function defied on a close interval I.First, this paper simply introduce the background and the development of the semiparametric errors-in-variables model, the strongly consistent and the asymptotic property are given through two stage estimator in semiparametric model. Thus, let us have on initial knowing about this concepts.Second, we extend the semiparametric model to the semiparametric errors-in-variables model, and estimate the unknow parameter and unknown function. Under some weak conditions, it is shown that these estimators are strongly consistent, p mean consistent, and asymptotic property. Furthermore, we give a result that the large sample confidence ellipsoid estimation and hypothesis testing ofβ.Finally, based on the unrobustness of least squares estimation, we introduce a robustness method M-estimation and give the consistent of parameter ofβ.