This paper constructs a set of confidence regions of parameters in terms of statistical curvatures for AR(q) nonlinear regression models. The geometric frameworks are proposed for the model. Then several confidence re...This paper constructs a set of confidence regions of parameters in terms of statistical curvatures for AR(q) nonlinear regression models. The geometric frameworks are proposed for the model. Then several confidence regions for parameters and parameter subsets in terms of statistical curvatures are given based on the likelihood ratio statistics and score statistics. Several previous results, such as [1] and [2] are extended to AR(q) nonlinear regression models.展开更多
This paper is devoted to a study of geometric properties of AR(q) nonlinear regression models. We present geometric frameworks for regression parameter space and autoregression parameter space respectively based on th...This paper is devoted to a study of geometric properties of AR(q) nonlinear regression models. We present geometric frameworks for regression parameter space and autoregression parameter space respectively based on the weighted inner product by fisher information matrix. Several geometric properties related to statistical curvatures are given for the models. The results of this paper extended the work of Bates & Watts(1980,1988)[1.2] and Seber & Wild (1989)[3].展开更多
In 1980's, differential geometric methods are successfully used to study curved exponential families and normal nonlinear repression models. This paper presents a new geometric structure to study multinomial distr...In 1980's, differential geometric methods are successfully used to study curved exponential families and normal nonlinear repression models. This paper presents a new geometric structure to study multinomial distributipn models which contain a set of nonlinear parameters. Based on this geometric structure, the authors study several asymptotic properties for sequential estimation. The bias, the variance and the information loss of the sequeatial estimates are given from geometric viewpoint, and a limit theorem connected with the obServed and expected Fisher information is obtained ill terms of curVature measures. The results show that the sequeotial estimation procedure has some better properties which are generally impossible for nonsequeotial estimation procedures.展开更多
文摘This paper constructs a set of confidence regions of parameters in terms of statistical curvatures for AR(q) nonlinear regression models. The geometric frameworks are proposed for the model. Then several confidence regions for parameters and parameter subsets in terms of statistical curvatures are given based on the likelihood ratio statistics and score statistics. Several previous results, such as [1] and [2] are extended to AR(q) nonlinear regression models.
基金Supported by the NSSFC(02BTJ001) Supported by the NSSFC(04BTJ002) Supported by the Grant for Post-Doctorial Fellows in Southeast University
文摘This paper is devoted to a study of geometric properties of AR(q) nonlinear regression models. We present geometric frameworks for regression parameter space and autoregression parameter space respectively based on the weighted inner product by fisher information matrix. Several geometric properties related to statistical curvatures are given for the models. The results of this paper extended the work of Bates & Watts(1980,1988)[1.2] and Seber & Wild (1989)[3].
文摘In 1980's, differential geometric methods are successfully used to study curved exponential families and normal nonlinear repression models. This paper presents a new geometric structure to study multinomial distributipn models which contain a set of nonlinear parameters. Based on this geometric structure, the authors study several asymptotic properties for sequential estimation. The bias, the variance and the information loss of the sequeatial estimates are given from geometric viewpoint, and a limit theorem connected with the obServed and expected Fisher information is obtained ill terms of curVature measures. The results show that the sequeotial estimation procedure has some better properties which are generally impossible for nonsequeotial estimation procedures.
