Quasi-regression, motivated by the problems arising in the computer experiments, focuses mainly on speeding up evaluation. However, its theoretical properties are unexplored systemically. This paper shows that quasi-r...Quasi-regression, motivated by the problems arising in the computer experiments, focuses mainly on speeding up evaluation. However, its theoretical properties are unexplored systemically. This paper shows that quasi-regression is unbiased, strong convergent and asymptotic normal for parameter estimations but it is biased for the fitting of curve. Furthermore, a new method called unbiased quasi-regression is proposed. In addition to retaining the above asymptotic behaviors of parameter estimations, unbiased quasi-regression is unbiased for the fitting of curve.展开更多
In order to construct estimating functions in some parametric models, this paper introducestwo classes of information matrices. Some necessary and sufficient conditions for the informationmatrices achieving their uppe...In order to construct estimating functions in some parametric models, this paper introducestwo classes of information matrices. Some necessary and sufficient conditions for the informationmatrices achieving their upper bounds are given. For the problem of estimating the median,some optimum estimating functions based on the information matrices are acquired. Undersome regularity conditions, an approach to carrying out the best basis function is introduced. Innonlinear regression models, an optimum estimating function based on the information matricesis obtained. Some examples are given to illustrate the results. Finally, the concept of optimumestimating function and the methods of constructing optimum estimating function are developedin more general statistical models.展开更多
基金Project supported by the National Natural Science Foundation of China (No. 10571093, No. 10371059)Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20050055038)+2 种基金the Natural Science Foundation of Shandong Province of China (No. 2006A13)the China Postdoctoral Science Foundation (No. 20060390169)the Tianjin Planning Programs of Philosophy and Social Science of China (No. TJ05-TJ002).
文摘Quasi-regression, motivated by the problems arising in the computer experiments, focuses mainly on speeding up evaluation. However, its theoretical properties are unexplored systemically. This paper shows that quasi-regression is unbiased, strong convergent and asymptotic normal for parameter estimations but it is biased for the fitting of curve. Furthermore, a new method called unbiased quasi-regression is proposed. In addition to retaining the above asymptotic behaviors of parameter estimations, unbiased quasi-regression is unbiased for the fitting of curve.
基金Project supported by the National Natural Science Foundation of China(No.10171051)and the Youth Teacher Foundation of Nankai University.
文摘In order to construct estimating functions in some parametric models, this paper introducestwo classes of information matrices. Some necessary and sufficient conditions for the informationmatrices achieving their upper bounds are given. For the problem of estimating the median,some optimum estimating functions based on the information matrices are acquired. Undersome regularity conditions, an approach to carrying out the best basis function is introduced. Innonlinear regression models, an optimum estimating function based on the information matricesis obtained. Some examples are given to illustrate the results. Finally, the concept of optimumestimating function and the methods of constructing optimum estimating function are developedin more general statistical models.
