For the generalized linear model,the authors propose a sequential sampling procedure based on an adaptive shrinkage estimate of parameter.This method can determine a minimum sample size under which effective variables...For the generalized linear model,the authors propose a sequential sampling procedure based on an adaptive shrinkage estimate of parameter.This method can determine a minimum sample size under which effective variables contributing to the model are identified and estimates of regression parameters achieve the required accuracy.The authors prove that the proposed sequential procedure is asymptotically optimal.Numerical simulation studies show that the proposed method can save a large number of samples compared to the traditional sequential approach.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
基金supported by the National Natural Science Foundation of China under Grant No.11101396the State Key Program of National Natural Science of China under Grant No.11231010the Fundamental Research Funds for the Central Universities under Grant No.WK2040000010
文摘For the generalized linear model,the authors propose a sequential sampling procedure based on an adaptive shrinkage estimate of parameter.This method can determine a minimum sample size under which effective variables contributing to the model are identified and estimates of regression parameters achieve the required accuracy.The authors prove that the proposed sequential procedure is asymptotically optimal.Numerical simulation studies show that the proposed method can save a large number of samples compared to the traditional sequential approach.
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.
