Semiparametric Ev Models With Two Estimates

The paper studies semi-parametric Errors-in-Variance modelHere is a p-dimensional parameter vector to be estimated, is an unknown function on [0,1] and is a p 4- 1 iid random error vector with mean 0 and variance unknown,U is an error in variance. is measurable directly on Rp x R1 but Xi is not, and are independent each other. This model is a class of EV model. In this model, regression function that variance yt is about is nonlinear, is not measureable directly and the measurable directly is X, that is errors-in-variance. The method of estimation is more difficult than the usual because x is not measurable directly. In first chapter, we define the first stage estimators for 0 and g by using kernel weight function, least square and two stage estimation under the additivity of the model, and then the paper proves that is the consistency and the approximate normal distribution, and is the consistency and the uniform consistency. In second chapter, we obtain the second stage estimators for 0 and g with the first stage estimators by using generated least square that is used in EV model. The second stage estimators are better than the first stage ones concerning variance, and meantime the paper proves that is the consistencey and the approximate normal distribution and gn is the consistency and the uniform consistency. In third chapter, we first give the two estimators a2, and CT for with the estimatorsobtained before, and then define the Bootstraps and of and by using method of resampling. We also prove that and are the consistency and the approximate normal distribation. and also study the characters of the Bootstraps a2 and dn and obtain some useful conclusions that are shown in theorem 1 and theorem9.