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.
